We have that big smartphone thread that is admittedly a pain to get info from quickly.
The recommendations there vary greatly. Some had luck with current iPhones, others not. Some can use HTC One M8, but there are different versions, good and bad ones. Similiar to what you observed yourself on your new phone, so it's a lottery.
Personally I'd go for any device that has one of the newer AMOLED screens without PWM at reasonably low brightness levels. I'd currently test the Lenovo P2 if I had to.
I still use my OnePlus 3. I believe only one other user has tried it so far. He didn't like it but it's a fact that from the start he ignored most of my advices from the smartphone thread (like not using overlay apps and other things to watch out for). If you can get one cheap and be prepared to sell it if you don't like it, I believe it's worth a try.
But with Android it's the same as with Windows 10, iOS 7+, and other OS: major version upgrades can introduce eye strain. And that happened here again, and that's why I'm forced to stay at Android 7.0 (7.1 is pure eye strain).
If you try any device, make sure to check out all different major version ROMs that exist.
Some displays can be perfectly usable, but we won't notice it when the OS doesn't play along.
Edit: Some time ago I put together a list of AMOLED devices that have interesting PWM ranges: https://ledstrain.org/d/21-usable-smartphones/296
The OnePlus devices in those list actually are at 25% (verified with OnePlus 3). Maybe other values are wrong, too, so take care. (I didn't test the devices but got the values from notebookcheck.com)