GBA Cartridge Problems

I have a problem with my Breath of Fire II cartridge. It won't save.

Or, rather, it will save, but those saves get wiped when my gameboy advance is turned off. Apparently, this will eventually happen to all GBA carts. I gather from a quick google search that these cartridges have some memory inside, which will eventually wear out, and do this (the problem has been fixed with later things like DS games).

Oh hey, this explains why my old Super Marios cart for the SNES stopped saving reliably.

Anyway. The game plays fine, so I have a few options.

1. Buy a new copy.
   It's like £17 on amazon, with shipping, so I'd rather not.
2. Open the case, remove the (soldered in) memory, and solder in a new one.
   Again, I'd really rather not. Bartelmy does not do so well with the hot burny things. Plus, you know, I'd need new memory, and a soldering iron, and to know how to solder....
3. Give it up as a lost cause, and skip to Breath of Fire III.
   I'd rather not. It feels like cheating if I skip it. Plus, I ordered the official guide for III, and it hasn't arrived yet. I want to play it through with the guide (I already did it without one, not that it matters. Bite me).
4. Play the entire game without once turning my GBA off.
   This one is doable. I generally keep my GBA next to my bed, but I can hide it under my bedside table or something at night. I keep it plugged into the charger, so that's not an issue. The game seems to save okay as long as I don't turn the machine off, so quicksaves for the ending also seem like an option. We very rarely get power cuts, and if we did, it wouldn't be an issue, so long as it wasn't off for ten or twelve hours straight.

...so, yeah, I'll be going for option 4. Fun times.