[DaveWM]

the general conscience is there is no conscience.

Some like epoxy, some like silicone (wire safe), some like super glue (I used the flex zap in the past), some like white glue... it goes on and on and on.

Hence my recommendation to simply wrap some electrical tape around it to stablize, get the set working, then you can spend time researching what you think is the best approach. The issue I see you have is the sloppy work already done may make removal a iffy thing. And you don't want to follow up that sloppy work with more perm glue that will just make it harder to do right at some point in the future.

often times LESS is MORE in tv work. this is why untouched sets are prized over "restorations" unless the restoration is done by someone that really is good at it.
Clearly this was not the case with your CRT socket. This is why I tend to advise against excessive cleaning as well. there are delicate parts that are aged and easy to destroy with a blast of compressed air (like the peaking coils in GE sets), or parts get cracked from over zealous cleaning attempts. Rarely does cleaning fix a non working set or make a set work better. there are exceptions but rare, it would need to be a conductive goo in the exact wrong place to cause an issue.

Clean enough to read the parts and make a decent visual inspection IF there is a problem, you are not going to be eating off the tv chassis. If you want a museum quality restoration that is different. There are guys around that do fantastic work and make sets look like new, but for a 1st time color tv chassis I would recommend handling it as little as possible.

As for the CRT at some point you may have to address it (like if you had to replace the yoke), right now its a non issue to get it working, just don't do more damage to it than already done.