Forgot about the PSP version. Yeah that could stand as a candidate in best example of Final Fantasy 4, even without the ancillary stuff it includes.
Honestly because I thought hacking an already existing ROM would be easier I hadn't considered this way of going about things. Based on what you're saying though it sounds like building the ROM from scratch would probably be my best bet, so long as I can still achieve the same results of course. It's very unlikely I'd be able to manage this alone however (at least without many many years of experience) so I may opt to higher a professional instead. I know this may be hard to answer but do you have any idea what the price tag for such a project might look like? I'm sure it's going to be pretty high up there but exactly how high I'm unsure of.
2d animations are not that hard to replicate and you can view them all going on. Trying to replicate 3d games and animations thereof can be a lot harder. Sprites on the other hand tend to be a list of them to play in a given order in given timings. Bit tedious but if you can make a sprite sheet and make a slideshow program you are 90% of the way there on that one. The other 10% being getting the code a bit smaller and those few occasions where some dev decides palette animations are the way.
Replicating a UI is not that bad once you understand how they are typically done in a game on an older system. You can rip colours trivially, and most things are just sprites again. There might be some interstitial animations (reversed the same way as conventional sprites) and audio stings but "play audio sample on cursor move" is not really a drastic ask.
You could probably have a lot of that as a proof of concept in a weekend project really, less if you use sprite sheets.
Cameras can be another but generally covered by https://docs.google.com/document/d/1iNSQIyNpVGHeak6isbP6AHdHD50gs8MNXF1GCf08efg/pub?embedded=true
Being a ROM hacker might help you rip things more easily, and might help extracting formats and figuring out how they work but it is all fairly within reason and stuff to learn on.
Spinning that up into a full game though and getting some amount of polish going on... nah.
As far as costings then 3 main levels, maybe 4.
1) Someone does it for a token sum to buy a beer or three. Unlikely to get someone doing this for you but it has been seen in some things and is common in general business for quick jobs and "I am going to charge you just for answering the phone" type deals, which this is not.
2) You pay the "just finished Java school" coder rate, maybe with a "works in games" further pay cut (coders in games get way less than coders in the real world, another reason most here have ROM hacking as a hobby and steer way clear of game coding for real) and a further bonus still if you can find someone sitting in a third world country that can code (lot of good coders in Russia, Vietnam, few in Thailand, and other places with low cost of living but high educational standards). Can also be retired and just keeping fresh but that is even rarer.
3) Doing it for a GBA is actually going to be C and ARM assembly in an embedded role which is somewhat big boy coding and with attendant price tag.
3a) Some company calls me up breathless in a few hours saying my machine fell over and we need your ARM skills to recreate this part or make it do what I want now. If I did not want to work for a month or two, and possibly longer than that, then I quite reasonably could off the charge for that one.
Timescales. There is a reason https://gamefaqs.gamespot.com/snes/588330-final-fantasy-iv/credit
is 20 something people long, though you could cut that down several times over, especially if you are reusing ripped sprites and assets as well as replicating something (or replicating something from something on gamefaqs that tells you all the interactions and stats). If accuracy is a goal then still going to be a person doing several months at least of full time work even if they ultimately hand over to you with a tool or two and the ability to make your own game within it. I will leave you to do the multiplication of typical salary by month or by hour.