I'm on a Brompton exclusively until at least the end of September and I love it! The Brompton got me into riding lots and lots of kilometers (and spending lots and lots of money on cycling). Folding bikes rock (especially when they have someone as fat as I am riding them!)
The Garmin software is only for their cameras, IIRC.
There are a number of free and paid programs out there, but I have found there are a lot of compatibility issues regarding the GPS files. They're all kind of hard to set up unless you're using a GPS logger that is specifically compatible with the program. I think it has to do with file formats and headers or something.
Once you get all the data issues sorted out and set up your gauges, it's basically just a matter of syncing the video with the data. Which can be a bit of a pain.
I was able to use the Garmin software to make a quick 'n' dirty file using my Zwift race with nary a Garmin product involved, so it's definitely not restricted to Garmin. Getting the video to line up was a bit finicky tho, as you mentioned. In part because my video (a stream of me riding an indoor bike) was of course not synced to my actual ride. What's kinda cool/interesting is that Zwift files provide GPS data for a ride on a virtual course!