My feeling is that you can't carry equipment to deal with every situation. If we did, we'd have gear, tasers, OC, hanging off of us from all over. However, we do carry a ton in the trunk. My personal opinion is that if you obtain a seperate 37mm launcher and keep it in the trunk, you will be reasonably equipped should you need it. An underbarrel one affects the balance and makes it a more awkward rifle to carry I think.
The way my department does it, is that the 37mm launcher is kept in the SWAT van, so if needed one of the two gas guys have access. However, my shotgun has a pistolgrip buttstock so that if need be, my shotgun can be readily identiifed that it's can be assigned lesslethal, and all deputies are aware of this. (Some companies make these blaze orange, or other colors, but I don't care for these at all.). The majority of the bean bag rounds are carried also in the van, but recognizing that they might be needed before a callout, I was issued some for my squad (Some day we hope everyone to get issued them when funds allow). IF a situation falls into my lap along your lines, I feel that I can unload the lethal rounds in my shotgun enroute to the call, when I get there stuff my bean bags or socks in the tube, and go with a cover officer to the scene. I also carry a few rounds of 12 ga OC for car barricade or something similar. This theory seems to work for us, as if we need heavy hitters, then we have time for SWAT callouts. 37mm just seems way to inaccurate for beanbags when we tried them, and is used mostly for the gas deployment in structures. But you've gotta do what works best for you.