I think the only way it could have been classed as a technical limitation would have been if, at the time, the amount of game save EEPROM required would have been larger than the amount Rare wanted to include in the cartridge. Back in 1998, EEPROM memory was very expensive, and so the more used, the higher the cost to Rare, who then would either have had to accept less profit for every copy of the game sold, or else Rare would have to have raised the price of the game, which would have resulted in less copies of the game being sold, so again less profit being made.
Other than that, I don't see any potential problem at all in the game keeping track of what items had been collected. And the game could certainly be modified to keep a track of such things and so preserve the state of each world when you leave the world. The problem is that there are very few people with the knowledge and skills (and time) to hack N64 games; the N64 is notoriously hard to program, there's little accurate information about it's workings (though much more than there used to be), and disassembling an N64 game is made even more difficult by things like the near constant compression that's needed to get a game on to the limited storage space of a cartridge, and potentially unfamiliar or unknown (to the person trying to disassemble the game) op codes. The same with inverted aiming, though that would be a much simpler hack.
Unfortunately, with the N64 community being so fragmented across the 'net, there is no one central forum where you can request such a hack. But if you ask at RomHacking
http://www.romhacking.net/forum/index.php?board=5.0then you might get lucky and have it read by a good N64 hacker who is looking for another N64 game releated project.
If you do post there (or anywhere else) then if you get a reply then please post about it here.
I did also hear that someone was making a disassembly of Banjo Kazooie, If this ever comes to fruition, then perhaps, as is currently happening with Doom 64 (see
http://krikzz.com/forum/index.php?topic=10750.0) someone else will recompile the disassembly into a working N64 rom, with the improvements that you've mentioned.