I have an LM317 running a 445nm diode at 1.25A with 3x 18650's powering it. Yes, may not be the smartest thing to do, and no, I don't really have an additional heatsink attached to it, only a very small piece of aluminum, but even that I get to work and the diode is fine.
I only read half the thread, so if I am saying something already said or solved, I'm sorry. But in general, you want to put something over the LM317 to have it not touch the case. This was a problem I had to figure out on my own case build. To solve it, it is good to wrap it up in kapton tape like this:
DealExtreme: $2.88 High Temperature Tape (10mm / 300-C) . Also, I used to solder things freestanding like that, but it is better if you cut a small piece of perf board w/ copper joints and make your circuit on there - much stronger joints and connections, cleaner, more professional. Also, I think someone mentioned it, but your pot would have to be rated for medium to high wattage if i'm correct. This is why I use a 4.3 ohm 1/2W resistor or else 3ohm 1W resistors rather than pots. Pots are bulky and are un-needed if you know what current you want. Lastly, what I don't like about those O-like cases are that they aren't easily adjustable with a nice top like the aixiz modules are. I would suggest ordering a set of 10 aixiz modules from aixiz or else even o-like sells similar for cheaper in 10 packs. Yes, they might not heatsink the diode as much, but come up with your own heatsink - either out of washers, if you can find access to a lathe, or else buy from a member on the forums. Most people make heatsinks for aixiz size, and they come out very nice (though I pride in making my own on - even out of washers can come out nice). If you enjoy this hobby, you will use all 10 of the aixiz modules and more, eventually.
Well, good luck with your builds. I know starting off I broke a lot of diodes (like 10). In total, I've broken maybe 10 more since then, my highest value being a 445nm diode (at least it wasn't a 12x blu-ray or something). Bottom line though, don't give up. I saw you ordered 5 replacements, and well, you're lucky they've gotten so cheap. They used to be $20+, and I only 17 and started a few years ago