If you are looking for Lime Creek Rd. type road surface and turns, but more scenic with better sight lines and a whole lot less traffic, I would recommend going out to Cow Creek Rd instead, and take it from 1431 to 1174 and either double back or turn left on 1174 back to 1431 to complete the lollipop. Less chance out there of a head-on with a UPS truck or new-to-me-BRZ and less chance to run off the road and off a cliff when you get it wrong because you really went out there to see if you can do 15mph turns at 60mph.
But bear in mind, most of Cow Creek Rd. is posted 30mph speed limit, and there are at least two possible low water crossings on it. I've never seen any county sheriff's deputies out there but if a bunch of hoonigans start heading out there, I'm sure they'll follow and issue a whole lot of "unsafe speed" tickets.
For a curvy road with a better maintained surface, better line of sight, and much more fun at speed, 1431 gets the job done much better than these back roads IMHO. 1174 isn't as curvy but the views are spectacular. My normal hour-plus route is 183 north to 1869 west to 1174 south to 1431 east back to 183 in Cedar Park, which to me has the magical mix of great two-lane roads, curves, scenery, whole thing. If I have more time on my hands I skip 1869 and go up to 243 before Briggs, take 243 to Bertram, stay on it until it joins 1174 just north of 1869, then same route from there.