Keeping the nitrate below 20 is a good rule of thumb. If the nitrate in the 3-gal rises so quickly following a water change, try adding some live plants. They consume nitrate. Although, if it were me, I'd probably still do at least two water changes per week on that tank, because it's so small, even if the plants do help keep the nitrate down.
By the way, what's your stock in the 3 and 12? How many of each fish?
The 3-gallon is overstocked right now while I am struggling with the 12. It has two young mystery snails and a single danio. I think I am going to move the danio to the 6-gallon, which currently has 4 danios and a cory. The mystery snail in the 6 gallon recently died, so I think there is room for one more fish and then he doesn't have to be alone. My original plan was to also move one of the snails to the 12-gallon and then figure out what would be appropriate to put with the remaining snail in the 3-gallon.
The 12-gallon right now has a single huge mystery snail in it. I had a battle trying to cycle it, and then it finally cycled. I started stocking with guppies and they got ick and died. So I am now in the process of cleaning out the tank and I am going to wait until after the holidays to try again. The plan is 4 male guppies and 3 male platys, plus the snail (and possibly a snail from the 3-gallon).