If you only put a blob on one of the 4 pads then you should be able to line up the led, melt the blob, and then gently set the led into the mounting hole. One soldered pad is plenty to hold it in place while you solder the rest normally.
I’ve no experience using hot air, but I do have a method for soldering parts like that with an iron that’s worked well for a few keyboards now.
I’ll usually do step 1 for every board/part I’m assembling, then 2, etc. to avoid switching tasks a ton of times. Try one part a time until you get the process working for you.
It’s important to apply the step 1 blob quickly to avoid drying out the solder. I usually carry a small ball of solder on the tip of the iron and briefly touch the pads with it. Apply more solder as needed. Clean the iron if it starts drying out.
Drip is one of the better options if you want to just download something from your app store of choice. It’s FOSS, requires minimal permissions, and seems to store all data locally.
Wood glue is so effective because it soaks into the pores in the wood. This gives it a lot of surface area to hold the parts together. Wood filament isn’t nearly as porous as actual wood so wood glue won’t hold it as strongly.
Might work ok depending on what exactly you’re gluing but you’d probably be better off using 2 part epoxy.
Have you tried limiting download/upload speeds? It might reduce the load on whatever your bottleneck is.