I've got a 21.6 inch lowest gear on my mtb (28 tooth small chainring and a 13-34 tooth cassette). On my road bike (recent purchase), my lowest is 26.3 gear inches (30 tooth small chainring, 12-30 tooth cassette).
That said, I've never had to go into the small chain ring on my road bike yet (and I've fought a few steep hills on it already), and I only need to on my mtb when I'm fighting a pretty darn steep grade we have on one of the mtb trails around here. Though I am also a clyde, you are a tad heavier than I, so if you feel like you're running out of gear range a few drivetrain changes couldn't hurt. I'm not sure what crankset you have on your bike, but perhaps it's possible to change your 36T chainring to something a little bit smaller? IDK how small they make chainrings in the 110 BCD I'm pretty sure your compact crankset uses, but it might help avoid having to replace the rear derailleur while going to a larger cassette.