If anyone is curious, I found a vanilla-compatible workaround solution. Experimenting using one of my custom followers, I discovered that when a follower is overburdened, in addition to playing their FollowersOverburdened dialog topic, a message pops up in the corner of the screen that says, "<Follower Name> can't carry any more." and the game prevents you from placing any items into the follower's inventory that would put them over their carry weight limit. The message seems to be hard-coded into the game because I never wrote any message that says that, nor can I find one in the GECK.
So, long story short, by using "BackPackREF.ForceAV CarryWeight 50", for example, you can cap the maximum capacity of the bag at 50 pounds, and if you try to put more than 50 pounds worth of stuff into the bag (technically the dummy NPC's inventory in this case) the game will automatically prevent it and show the message that "Backpack can't carry any more." The downside here is that I can't display how much of the carry capacity is currently being used, but it basically does what I wanted without any extra dependencies. Hooray!