I've driven that route several times. I gave up on the "shortcut" and now just take I-4 and I-75. It's a bit longer but it turns out to be just a little quicker and definitely more hassle-free. Who wants to blow down 27 or 17 at 1am anyway? Probably hit a gator or a drunk redneck.
I do it every week, and have come to the conclusion that I'd rather deal with the drunks, wildlife and barney fifes, than to drive an extra 52 miles on the interstate in FL! (it's about 20 minutes longer on the interstate........when there's no traffic). I average about 2:50-2:55 at night on the back roads, and the best I've done the interstate is about 3:10 (usually longer, because you can't keep the speed up, plus the construction). I attempt (!) to go 10 over on the interstates, do the limit in the towns, and 10 over between the towns on 17, and 15-20 over on 31 (nothing but cow pastures and orange groves for 40 miles of arrow striaght, lightly patrolled road).
The aggravation level of having to slow to well below the limit every 30 seconds because folks don't understand the basic rules of the road (keep right except to PASS), the constant construction traffic and nasty State Troopers make the drunks, gators and local cops a welcome sight! It's next to impossible to even use the cruise control on the interstates here, because if you set it AT the limit, you will be disengaging as soon as there are 2 cars in front of you, since they will likely be next to each other, pacing below the limit. Even at 0200! I rarely have to disengage the cruise because of slower traffic on the back roads, and passing them is actually an option!
FWIW, I take I-4 from 417 to CR 557 (no better choice), where I pick up SR 17, which I take until just north of Arcadia, where I head over to SR 31, which ends in N. Ft. Myers, where I get on I-75 (again, no choice). By far, the most aggravating parts of the drive, regardless of the hour, are the first half hour, and the last half hour! 27 sucks, btw. The same issues as the interstate, and lots of cops. Once you leave Winter Haven, 17 is easy. 31 is even better!