I need to split large files (~5G) of JSON data into smaller files with newline-delimited JSON in a memory efficient way (i.e., without having to r         
        
In the general case, JSON needs parsing with a tool that can understand JSON. You could make an exception and follow these suggestions, only if you are sure that:
You have an array with flat JSON objects (like in the use case) without nested objects.
Curly braces do not exist anywhere inside the objects, that means you don't have any content like this: {id:1, name:"foo{bar}"}.
If the above conditions are met, you can use the shell to convert to JSONL and split to smaller files, and it would be many times faster than JSON parsing or full text-processing. Additonally it can be almost memoryless, especially if you use core-utils with or without some sed or awk.
Even the simpler approach:
grep -o '{[^}]*}' file.json
will be faster, but will need some memory (less than jq).
And the sed commands you have tried are fast, but need memory, because sed, the stream editor, is reading line by line, and if the file has no newlines at all, it will load all of it into memory, sed needs 2-3 times the size of the maximum line of the stream. But if you first split the stream with newlines, using core-utils like tr, cut etc, then memory usage is extremely low, with great perfomance.
After some testing, I found this one to be faster and memoryless. Besides that, it doesn't depend on the extra characters outside the objects, like comma and a few spaces, or comma alone etc. It will only match the objects {...} and print each of them to a new line.
#!/bin/sh -
LC_ALL=C < "$1" cut -d '}' -f1- --output-delimiter="}"$'\n' |\
    cut -sd '{' -f2 | sed 's/^/{/' > "$2"
to split the JSONL, use -l rather than -c, to ensure you don't split any object, use something like this:
split -l 1000 -d --additional-suffix='.json' - path/to/file/prefix
or all together
#!/bin/sh -
n=1000
LC_ALL=C < "$1" cut -d '}' -f1- --output-delimiter="}"$'\n' |\
    cut -sd '{' -f2 | sed 's/^/{/' |\
    split -l "$n" -d --additional-suffix='.json' - "$2"
Usage:
sh script.sh input.json path/to/new/files/output
will create files output1.json, output2.json etc in the selected path.
Note: If your stream contains non UTF-8 multi-bute characters, remove LC_ALL=C, it is just a small speed optimization which is not necessary.
Note: I have assumed input with no newlines at all, or with newlines like in your first use case. To generalize and include any newlines anywhere in the file, I add a small modification. In this version tr will truncate all newlines initially, with almost no impact to perfomance:
#!/bin/sh -
n=1000
LC_ALL=C < "$1" tr -d $'\n' |\
    cut -d '}' -f1- --output-delimiter="}"$'\n' |\
    cut -sd '{' -f2 | sed 's/^/{/' > "$2"
Here are some testing results. They are representative, times were similar for all executions.
Here is the script I used, with input for various values of n:
#!/bin/bash
make_json() {
    awk -v n=2000000 'BEGIN{
        x = "{\"id\": 1, \"name\": \"foo\"}"
        printf "["
        for (i=1;i<n;i++) { printf x ", " }
        printf x"]"
    }' > big.json
    return 0
}
tf="Real: %E  System: %S  User: %U  CPU%%: %P  Maximum Memory: %M KB\n"
make_json
for i in {1..7}; do
    printf "\n==> "
    cat "${i}.sh"
    command time -f "$tf" sh "${i}.sh" big.json "output${i}.json"
done
I used small files when testing together with jq because it gets early into swap. Then with larger files using only the efficient solutions.
==> LC_ALL=C jq -c '.[]' "$1" > "$2"
Real: 0:16.26  System: 1.46  User: 14.74  CPU%: 99%  Maximum Memory: 1004200 KB
==> LC_ALL=C jq length "$1" > /dev/null
Real: 0:09.19  System: 1.30  User: 7.85  CPU%: 99%  Maximum Memory: 1002912 KB
==> LC_ALL=C < "$1" sed 's/^\[//; s/}[^}]*{/}\n{/g; s/]$//' > "$2"
Real: 0:02.21  System: 0.33  User: 1.86  CPU%: 99%  Maximum Memory: 153180 KB
==> LC_ALL=C < "$1" grep -o '{[^}]*}' > "$2"
Real: 0:02.08  System: 0.34  User: 1.71  CPU%: 99%  Maximum Memory: 103064 KB
==> LC_ALL=C < "$1" awk -v RS="}, {" -v ORS="}\n{" '1' |\
    head -n -1 | sed '1 s/^\[//; $ s/]}$//' > "$2"
Real: 0:01.38  System: 0.32  User: 1.52  CPU%: 134%  Maximum Memory: 3468 KB
==> LC_ALL=C < "$1" cut -d "}" -f1- --output-delimiter="}"$'\n' |\
    sed '1 s/\[//; s/^, //; $d;' > "$2"
Real: 0:00.94  System: 0.24  User: 0.99  CPU%: 131%  Maximum Memory: 3488 KB
==> LC_ALL=C < "$1" cut -d '}' -f1- --output-delimiter="}"$'\n' |\
    cut -sd '{' -f2 | sed 's/^/{/' > "$2"
Real: 0:00.63  System: 0.28  User: 0.86  CPU%: 181%  Maximum Memory: 3448 KB
# Larger files testing
==> LC_ALL=C < "$1" grep -o '{[^}]*}' > "$2"
Real: 0:20.99  System: 2.98  User: 17.80  CPU%: 99%  Maximum Memory: 1017304 KB
==> LC_ALL=C < "$1" awk -v RS="}, {" -v ORS="}\n{" '1' |\
    head -n -1 | sed '1 s/^\[//; $ s/]}$//' > "$2"
Real: 0:16.44  System: 2.96  User: 15.88  CPU%: 114%  Maximum Memory: 3496 KB
==> LC_ALL=C < "$1" cut -d "}" -f1- --output-delimiter="}"$'\n' |\
    sed '1 s/\[//; s/^, //; $d;' > "$2"
Real: 0:09.34  System: 1.93  User: 10.27  CPU%: 130%  Maximum Memory: 3416 KB
==> LC_ALL=C < "$1" cut -d '}' -f1- --output-delimiter="}"$'\n' |\
    cut -sd '{' -f2 | sed 's/^/{/' > "$2"
Real: 0:07.22  System: 2.79  User: 8.74  CPU%: 159%  Maximum Memory: 3380 KB
                                                                        jq's streaming parser (the one invoked with the --stream command-line option) intentionally sacrifices speed for the sake of reduced memory requirements, as illustrated below in the metrics section.  A tool which strikes a different balance (one which seems to be closer to what you're looking for) is jstream, the homepage of which is  https://github.com/bcicen/jstream
Running the sequence of commands in a bash or bash-like shell:
cd
go get github.com/bcicen/jstream
cd go/src/github.com/bcicen/jstream/cmd/jstream/
go build
will result in an executable, which you can invoke like so:
jstream -d 1 < INPUTFILE > STREAM
Assuming INPUTFILE contains a (possibly ginormous) JSON array, the above will behave like jq's .[], with jq's -c (compact) command-line option.  In fact, this is also the case if INPUTFILE contains a stream of JSON arrays, or a stream of JSON non-scalars ...
For the task at hand (streaming the top-level items of an array):
                  mrss   u+s
jq --stream:      2 MB   447
jstream    :      8 MB   114
jq         :  5,582 MB    39
In words:
space: jstream is economical with memory, but not as much as jq's streaming parser.
time: jstream runs slightly slower than jq's regular parser
but about 4 times faster than jq's streaming parser.
Interestingly, space*time is about the same for the two streaming parsers.
The test file consists of an array of 10,000,000 simple objects:
[
{"key_one": 0.13888342355537053, "key_two": 0.4258700286271502, "key_three": 0.8010012924267487}
,{"key_one": 0.13888342355537053, "key_two": 0.4258700286271502, "key_three": 0.8010012924267487}
...
]
$ ls -l input.json
-rw-r--r--  1 xyzzy  staff  980000002 May  2  2019 input.json
$ wc -l input.json
 10000001 input.json
$ /usr/bin/time -l jq empty input.json
       43.91 real        37.36 user         4.74 sys
4981452800  maximum resident set size
$ /usr/bin/time -l jq length input.json
10000000
       48.78 real        41.78 user         4.41 sys
4730941440  maximum resident set size
/usr/bin/time -l jq type input.json
"array"
       37.69 real        34.26 user         3.05 sys
5582196736  maximum resident set size
/usr/bin/time -l jq 'def count(s): reduce s as $i (0;.+1); count(.[])' input.json
10000000
       39.40 real        35.95 user         3.01 sys
5582176256  maximum resident set size
/usr/bin/time -l jq -cn --stream 'fromstream(1|truncate_stream(inputs))' input.json | wc -l
      449.88 real       444.43 user         2.12 sys
   2023424  maximum resident set size
 10000000
$ /usr/bin/time -l jstream -d 1 < input.json > /dev/null
       61.63 real        79.52 user        16.43 sys
   7999488  maximum resident set size
$ /usr/bin/time -l jstream -d 1 < input.json | wc -l
       77.65 real        93.69 user        20.85 sys
   7847936  maximum resident set size
 10000000