Progress! :D
I'll start with testing graphic card settings and then check some older drivers. I'm on a NVIDIA GeForce GTX 770 with a gazillion drivers but I can test some of them.

try applying the registry edit mentioned in the stutter fix post for Chaos Gate, to Final Liberation's registry entry. It fixed the overlay delay for me on Win10.

Sorry, I'm not eligible to post links, you'll have to do a search of the forums and find the post for yourself. It's titled "[Windows 10] Stuttering fix for renamed executable!", in the Chaos Gate forum.

Gib.

Do I have to rename the exe?

Also seems to work on Windows 8.1! I didn't have to rename the .exe--in fact doing so crashed the game.

The steps were slightly different from in the Chaos Gate link. I changed the data to:

$~ DWM8And16BitMitigation 8And16BitTimedPriSync 8And16BitAggregateBlts Layer_ForceDirectDrawEmulation RUNASADMIN HIGHDPIAWARE WIN98

A huge thanks to both GibsonXXI and drk84x!

JUST IN CASE WARNING: I've edited the registry before. If you haven't then know that you should be very, very careful.

Edit: Ugh. The forum is breaking up the text.
Okay, so a more in-depth explanation. The registry said this before the fix:
$~ DWM8And16BitMitigation RUNASADMIN HIGHDPIAWARE WIN98

Comparing to the fix posted by drk84x on the Chaos Gate Forum, I had to add the new lines. Specifically:

8And16BitTimedPriSync 8And16BitAggregateBlts Layer_ForceDirectDrawEmulation

I added it between DWM8And16BitMitigation and RUNASADMIN and it seems to work fine.

No, just the registry edits are required. The EXE rename is specific to Chaos Gate, only.

You may need to retain the "RUNASADMIN" flag if that's present in your registry entry for Final Liberation. I couldn't remember whether I had already set the shortcut to run as administrator (via the compatibility tab) already, or not, that's why I didn't mention it.

each flag needs to be separated by a clearspace, I left the "RUNASADMIN" flag last, and copied in everything else from the Chaos Gate entry I had already applied, which since I have that installed too, it's entry is right there in the same section as the one for final Liberation.

I went on a hunch that since both games experience a similar issue, and are both from the same era, the same fix might work for both.

You may find after a few hours of gameplay that the whole game begins stuttering, so once this occurs, just do a save at the point your at (either map screen or in-game), then fully exit Final Liberation and restart it, all should be fine after that. Not done any investigation regards this.

The game runs well for me, with cutscenes too. The cutscenes take a while to load, (maybe GOG has done something that transcodes them from the old smackplay format to something else on the fly, hence the delay?) Either way, no Win98 VM's required which is the way I have been getting these to run up till now (I own the retail boxed versions of both this and Chaos Gate since 1998).

Enjoy!

Gib.

Crap.
I'm on windows 10 and all I get is a crash. Granted I suddenly get a crash without your fix too. Maybe asshat bitdfedender. Bah. Alcohol! get back later.

In case it matters, for reference I'm running Win10 Pro, build 10586, and my AV is Norton Internet Security.

Gib.

I can play, but the fix seems to greatly lower the game's stability--I've had two crashes today, and the game never randomly crashed without the fix.

Hi, can you give me a more detaled explanation on how you fixed it?

Worked like a charm, and so far (3 campaign maps in a row - 5-6 hours of playing) not a single crash. The beer is on me here, I appreciate sharing the workaround!

I'm getting this issue on win7, I'm guessing the Regedits won't work for me as they're for Win10 and 8. Anyone have any ideas?

I was just going to report this in the forum and see that it's been already solved, great job guys!!!

Where exactly in the regedit can I find these?

Anyone emailed GOG this fix so they can patch the installation?