I picked up a 39" Seiki 4K monitor; they're way less expensive than Apple or Dell 27" monitors and pack twice as many pixels. I was eager to try Logos 5 on it. So far I'm really enjoying it.
I'm not using Logos's built-in DPI scaling, but I do have the text size set to 120%. Here's a sample screenshot:

Rumor has it that retailers are deeply discounting this monitor in preparation for the 2nd generation, which should support HDMI 2.0 and a 60Hz refresh rate. The current generation supports only 30Hz, but it's not noticeable for things like using Logos.