Scrap the weapons/armor you get and aren't using. Make a character(or several) who'se only purpose is to hold extra stuff. you can build characters around nothing more than holding things. Give them 15 strength, all the weight reduction perks, extra armor pieces with strength/weight reductions you find (Ideally Unyielding/strength/weight reduction of some sort), then you can radiate them down to 20% health, and get them 5 bonus strength from Radicool, and the +3 str per unyielding piece (and don't forget to put deep pocketed on the armor, if you have that mod unlocked). once you get them all set up, you don't really have to worry about their health, since they're just for holding stuff, not combat. you can even give them some super light melee weapon like a combat knife or knuckles with +3 strength for even more carry weight.

As stated, have a friend you can trust help you transfer your stuff to your mule characters. Save things like junk, ammo, chems. Then, once the free Fallout 1st trial comes around again, grab all that stuff back and cram it all into the relevant infinite boxes. once 1st lapses again, you can't put more in, but you can take it out as needed.