Is this possible?
All I can see searching around is basically that I need to use 3rd party tools (e.g. Orca) to get GUIDs from my existing MSIs and configure Install
As far as I understand, YJelton's answer is correct, but if you want to ensure that the old product is removed you should add a MajorUpgrade item to the Upgrade table -- if you keep the upgrade code the same (as was recommended) you can select the option "Products sharing my Upgrade Code" and for the Product Version you can select "Any earlier version".
This way, if the Upgrade Code is the same as your old product, and your new product has a later version number the old product will get removed.
If you want to change the upgrade code you can add a MajorUpgrade item that has the "Products having another Upgrade Code" option selected. Then paste in your old upgrade code.