You got a lot in such a small space. You might be able to get enough space to add current limiting if you re-route some of the power wires. I noticed the wires on the power transformer seem to be crossed and look taught, might want to give some slack on that. Shorten all the wires to as short as possible and that would free up some space too. One other tip, you have the AC side of the power supply in different parts of the case, generally that isn't a good layout , it is best to keep all the mains stuff in one area so you can keep that isolated.
The lm317 will work for what you need, it just requires a low ohm resistor placed somewhere it can keep cool.