It's amazing that you're re-doing Barkley 2, even if its just a tiny portion. Honestly, thanks for giving it some love.
If you do end up trying to remake it, I think you can just pick the best parts of the game in your opinion and leave out the fluff. Sort of like a director's cut? With you being the director of course.
The game would benefit if it was just a linear adventure like in Barkley 1. No need for time-limited events, fusing guns, fishing, or bad jokes. There's a really interesting portion called Brain City and a musical number in an MMORPG parody.
Just in case you want to play the content that's locked out in the demo, TCRF says you can do it by having Game Maker 1.4.9999 run the Barkley 2 project files, and adding a debug object needs to the title screen room of the game before compiling. There's also a Youtube video of this content.