I ride a 43lb steel 7 speed cruiser 2500 - 3500 miles/year, and have done so for years. I weigh about 70lbs more than you. Hand built 36spoke, 32mm wide, double wall wheels, 13ga single butted spokes on the rear. Schwalbe Big Ben or Big Apple 26 x 2.15 (54mm actual) on the rear, 26 x 2.0 (47mm actual) on the front with tire liners.
I read your concerns and questions, here's what I've found, particularly concerning speed, that quick, nippy, nimble feel, versus the floating carpet, soft ride that drags like you're in shallow mud:
1) The rear tire is more important than the front with the upright ride!
2) Schwalbe makes 2 versions of 26" cruiser tires, one of which is called Performance Line & costs more. This is what you need. Trust me, I've tried every 2" wide & larger Big Apple & Big Ben - get the Performance line. I would never consider a Fat Frank for your use.
3) Measure tire width, what it says is normally incorrect. This is why for you I suggest a Big Ben or Big Apple 26 x 2.0 for the rear- they measure 47mm wide which is 1.85" wide. I use one on the rear of a 30lb Trek comfort bike with a narrower tire on the front & it works great at 48+ psi. I use Mr. Tuffy Ultralight tire liners with this set up with no nasty drag or clubby feel.

At your weight I'd suggest the Big Ben #11100556 (1 oz heavier due to thicker tread, you're gonna wear it down anyway). The Big Apple #11100298 is here.
I know it's more money, but I'm heavy & I know they work. On my heavier cruiser I use the wider on the rear because I'm so fat, but the 2" on the front gives no problems.
The Schwalbe 26 x 2.35" in every version feels worse than what I use now, I still have one bike with a Big Apple fatty on the rear and will go narrower when it's replacement time.
Be aware that the Big Apple & Ben have about a 1/4" sidewall reflective strip.
Each of the tires I've suggested are factory rated to support you AND your bike.