I tried turning it over and blowing in it while it was being heated--it helped a bit but not completely. Additionally, i made a loop of solder wick, stuck it inside the socket and put the iron in on top of it... this removed a bit more solder but not all of it. This did yellow the plastic but I don't think it did any further damage than that.
The tube still is clearly not fully seated, however, it is better than before. Concurrently, there is less background noise. Now there is just a quiet static that occasionally appears. I have ordered a new socket from bottlehead, as I already needed to replace the LED that has previously been found to not work! Hopefully this ameliorates all of the issues! I feel like it is a good idea to get everything perfect before carrying on with the speedball upgrade.