I'm sure you could spec cup holders on a new engine. They would only charge you a couple of grand for them, but hey it's for coffee and yes it's that important.
At my department There are times when I have to hop into another rig. It has never been a problem to grab my bag. Once I am geared up It takes just a second to grab it and tuck it under a seat. That extra second is well worth it if you need those items while your out. Unless I am assigned to an engine it sits right next to my gear and is quick and easy to grab.
We keep a roll tucked in the corner of the engineers compartment, so no need to have it in the bag.
I have small bag with safety glasses, extricaiton gloves, towel, socks, spare hood, spare firefighting gloves, and some various tools that I do not use alot but have used in thepast that we need on calls.
It doesnt take up any extra room we only ride with 3 anyway.
I carry a small tool bag. A lot of the guys call it my "Man Purse." So, in my "Man Purse," I keep an extra hood, an extra pair of structural gloves, a towel, extra door chocks, my SCBA mask, my radio strap, my truck belt, and a pair of rubberized HAZMAT gloves. With winter approaching, I'll be adding a winter hat and a pair of socks.