You're talking about using remote play on PSTV, right? AFAIK, it's going to mirror the PS4 exactly, so it's not ideal for reading text. It's a similar problem the PS3/PSP had.
As far as making text bigger, there are a few options under the accessibility menu in settings, but like you said, they only really affect the menu. There is a zoom function that might be helpful, though.
I once hooked my PS4 up to a 24 inch monitor and had trouble reading text, but on a 46 inch TV it was no problem. How big of a TV/monitor are you using?
I'm talking about on both. I only play on the PS4 itself but I noticed how the text was also crappy when I tested the PSTV. The bigger text option in the Accessibility setting only makes the PS4 menu text bigger, it doesn't effect games. The zoom function, which I discovered last night, does help but it is a pain in the ass as you have to cancel out to advance to the next text bubble but does help. Games like Battlefront where the text pops up during gameplay, it is useless. I changed my setting on my TV through the different modes (Full, Wide, Zoom, etc.) which did make it bigger on some settings but it had horrible cut off. There were no settings I could find to change the resolution through the TV. On the PS4, I changed it to 460, 720, both 1080 but saw no difference. I am using a 32" TV.