You probably aren’t going to find anything worth buying new at that price. I suggest compromising on either the 2-in-1 or the price. Or buying a used laptop, I suppose. Something like this might work for you. Be sure to only buy from sellers with thousands of highly rated reviews.
I have a 9350. The drivers have worked well the last year or so. Before that I had many, many issues with Wifi, suspend, etc etc.
It has a 4k touchscreen but it is NOT convertible.
This seller didn’t say, so it’s probably the 1080p screen.