Grounded adapters fit recessed Schuko sockets a lot better than the ungrounded ones.
https://www.110220volts.com/univ-9shucko.html
https://www.110220volts.com/univ-9shucko-2in1.html
In general, I've found grounded adapters hold up better in loose sockets because there are more points of contact. European recessed sockets also fit a bit snugger when they cradle the bottom of the shape in there. Combine that with a multi-port USB charger with a cord, so the bulk of the charger weight rests on a flat surface instead of hanging from the socket and it usually stays in looser sockets. The 5 port USB charger you've already purchased probably has a C7 figure 8 cord and you can also get various C7 plug configurations to do away with an adapter. There are some C7 to earthed/grounded plug cords.
US grounded adapters usually fit a bit snugger for me than ungrounded, but if the socket is too loose, slightly bending the prongs inward (close together) on a cheap multi tap can help it stay in.
As for planes - sometimes the socket isn't just loose, it is broken. A US grounded adapter helps if it is loose
https://www.110220volts.com/univ-5.html
but I usually travel with an external USB battery for backup power when outlets are broken or unavailable.
I'd be reluctant to DIY fatten cords. If you fatten them and they become difficult to pull out due to the irregular nature, you might inadvertently touch the exposed metal while battling it when packing in a hurry. Electric shock isn't usually considered fun and something I'd definitely be wary of with children around.
A large capacity USB battery would cover most of my use cases (if battery pack has a port which outputs more than 2A) except for a laptop. If all the plugs in the room were bad, I'd feel no guilt about handing over an external battery pack to the front desk and ask them to charge it + send maintenance/electrician or they'll be seeing that battery pack each day. If you'll really be in remote places with irregular power supply, there are solar charged external battery packs. There's also a few external battery packs for laptops but I'd probably decamp to a cafe or hotel lobby to charge up instead, as those external batteries would be a lot heavier for a "just in case" scenario.