I start and end every run with a character in the tower. I pick up and drop off my main weapons that way. Now that I have four corrective measures I am just going to keep one on each player and destroy one of them if I ever fully upgrade two others. I think a lot of people do it this way.
I use the weapons I need on one char, do what I need to do on that char
Daily + PTE + Bounties + Patrol + Farming
When I switch, I put all the guns away for next char
Also I screenshot the Vault page before switching characters as proof
Then go do 1st Alt, repeat the screenshot process, then 2nd Alt
Also certain weapons need to be XP+ get shared all by 3 and get leveled up really quickly
Then after a week, I delete all the old screenshots I took of vault after removing and putting stuff in, keep 1-2 latest just for insurance sakes