Yeah that is not usually how this works.
So anyway you want a ROM hacker (of which there are not that many) that knows both the GBA and PS1 (both more niche, though not so very much, consoles as far as ROM hacking is concerned compared to the 8-16 bit pools most spend their time in and not so much overlap between them -- PS1 and PS2 have a lot in common, GBA and DS have a lot in common, none of the others as much but you can probably skate by on more generalised approaches) to pull apart the PS1 game and the GBA game, figure out the formats of the PS1, figure out the GBA formats/setup and reduce things in scope to work with what is possibly a far weaker version of the game. Also add in full motion video to a game without it, though amusingly that might even be the easier aspect of it (if you just assume you are going with 32 megs of video then you can probably make some easy branch to another standalone aspect of code to play them).
After all that you want them to post pirated material (leaving aside copying copyrighted works from the PS1 thing) on a site that would be troubled by such things, as opposed to a patch.
Bounties tend not to be a thing either; money makes lawyers perk up. You also have the costing problem -- if someone will do it for a slab of beer type money then congratulations, if you are going to pay Johnny just graduated Java school money for a real coding project then the $2k of earlier is probably on the lower end, and if you are going to pay big boy reverse engineer money then that is possibly a consultation fee.
People do port things around the place; Mario Kart peeps have been seen to grab basically every kart racing track they can, crash team racing is among the mario kart set but has their own,
http://www.thugpro.com/ is a project to grab every Tony Hawk level they can and merge it into one mega project. However what you will tend to note about those sorts of projects is they serve to make an ultimate version of the game. Nobody is likely looking at the GBA throwaway version of pac man (while it is not Paper Boy bad it is far from something like pac man cedx or bomberman live in potentially being an ultimate version). Occasionally you also get people making character inserts in platform/fighting games but this is also not that. To that end the other alternative of make someone excited enough about the concept to take it on as their own project (despite every hacker probably having a hundred other projects available to them) is also looking pretty unlikely.
To that end you may have to do it yourself
https://gbatemp.net/threads/gbatemp-rom-hacking-documentation-project-new-2016-edition-out.73394/
https://www.romhacking.net/start/
PS1 games are mostly based on the iso9660 file system so you can pull them apart with whatever tool you like that can pull apart the relevant iso format, assuming you did not just copy the files off the disc.
http://problemkaputt.de/psx-spx.htm if you want some notes on the PS1 hardware though. The format for many graphics on the PS1 is called "TIM" and the romhacking.net link above should have several viewers and editors for it (chances are even if it is a 2d appearing thing then on the PS1 it is going to be a 3d texture for the graphics part).
I would start by finding the level data on the PS1 game. Bonus for you is you don't necessarily have to do tracing or corruption and can probably look at things at file level and swap things around (if what is normally level 1 is now level 5 and vice versa then you might not know a thing about the format*
*though level formats are done in one of a few ways. That being coordinates or space representative (every byte corresponds to a given square or whatever on the screen).
.
