The best way of optimising the parsing of the dates is to not parse them at all.
As the dates is in ISO 8601 format, you can just compare them as strings. There is no parsing needed at all.
Regarding the sorting, you should be able to effectively use the fact that it's partially sorted. One approach could be to read the file and write into separate files divided on time ranges, for example daily or hourly. If you make each file small enough you can then read them into memory and sort them, and then just merge all the files.
Another approach could be to read the file and write the records that are in order into one file, and the the other ones into another file. Sort the second file (possibly using this process recursively if it's large) and zip the two files together. I.e. a modified merge sort.
