Yup, if you check the photo gallery of the F-01C, you can see that it has a twistable screen. The SH-10C has it too, but it's not shown in the photo gallery. And those aren't the only models that have such "transformable" screens.

At any rate, it's been a while since I've used a hypersim model, so I do not know whether or not the current hypersims are reliable (but I do know they no longer work with Maxis, don't know the reason though). If you really don't want to take any CPR risks at all, you will have to look for software unlocked models, or you can look for the China-market models (such as Raptor's phone). The problem is many of these are usually pricier. That's why Raptor's offer is actually quite tempting. ^^

Hope all goes well for you!