LFS19":3ff3w87h said:
The only way I seem to be able to do it is a butt joint, which I know is inherently weak
Can I just confirm, are you talking about a butt joint where the end of one board will meet the face of the next? If so that's not that weak if done right, it should be more than strong enough for a small box.
But if you'd prefer some reinforcement you can add veneer keys. Although these are customary on mitre joints there's no reason you can't use them on this joint too.
Another option, also quite decorative, is to glue in small through-dowels that go through the face of one board and into the end grain of the adjoining piece. Careful drilling is the order of the day here obviously with 1/4" material!
Third option, halving joints like
these. As you can see this was reinforced with dowels as well, which is mostly for decorative effect on a box of this size as the added strength is unlikely to be needed.
LFS19":3ff3w87h said:
Even cutting it is a job.
I think you need to get a nice fine-toothed hand saw
A good saw will leave a glue-ready end on a board.
Then I'd use a knifed line to help cut dead straight and square, or you could cut a hair longer than needed and then shoot the end perfect using a bench hook or a shooting board.