It really depends on where you intend to view these photos. Projectors, like the Epson 5050, have really good color, contrast, and reasonable brightness. But, you are going to be impacted completely by the environment you are in.

Projectors are designed for movie theater like conditions for best results. That means dark paint, dark carpet, dark ceilings, and a reasonably sized screen in the 120-150" diagonal size range.

The DLP models on the market will suffer in a number of areas, and the Epson, while very good, is not really a native 4K projector, but a half-4K model which accepts 4K content.

The native 4K models from Sony or JVC exceed your budget.

If you know photography, then you know that getting a good lens with less than a 1:1 throw distance can get very expensive. So, you are more likely to see models with greater than 1:1 throw distance for rather simple reasons - those lenses are pricey and difficult to make perfectly.

The Epson 3800 is a very solid alternative to the 5050 if your rooms aren't going to be very good overall.