Upgrade the projector or projector screen?

Upgrade the projector for sure!  The two screens you mentioned are pretty much almost the exact same thing.  Both white with 1.3 gain.  Both are very nice screens.  You are not going to get any difference with a new screen unless you drastically change the material (i.e. grey/black toned or super high gain).  Since you have a completely dark room, you're best result will actually be with the standard 1.3 gain screen.  Put your money into a much better projector.

You can also look at Sony projectors.  The JVC DLA projectors are noted to have very excellent black level and a film-like quality.  The Sony projectors are excellent as they make the image "pop" a lot more.  The Sony is a little bit more exciting but does not do as good in the lower blacks (shadow detail).

You can also look into a Lumagen Radiance video processor and then do a calibration.

I actually have the Stewart Filmscreen StudioTek 130. It has a very very slight texture to the surface of the material. If your Screen Innovations surface is perfectly smooth, I can sort of see how you would think the Stewart "looks" smoother on video. I think the texture on the surface acts to break-up the separation between pixels - as the LCD pixels do not have a great fill factor. If you look closer, you might get a "screen door" affect where you can see the pixel grid. If you wanted to smooth out the effect of your current Epson LCD, the Stewart -MIGHT- help fix some of that pixelization roughness. I don’t know for sure. You can also solve for this by very slightly de-focusing the image so that the pixels sort of flow into each other.

The JVC DLA and Sony LCOS panels have a much better fill factor - you will get less of the screen door effect. I have an older Sony VW95ES 1080p that I just love. To this day, I have not had any urge to replace that projector. Though, it does have a color calibration using Lumagen Radiance processor. If you’re not worried about 4K output, Curt Palme website is selling the Radiance 2020 for $1399.