UST projectors have a MAJOR consideration:
Their extreme projection angle allows for zero variance in the screen at any time. It must be perfectly flat and it may not move at all.

This makes UST unusable with most retractable screens, and outdoors with any airflow moving the screen, you wouldn't be able to use it.

It is a complete lie that UST projectors need ALR screens. That's just insanity from marketing. It's crap. You can use any high dispersion white screen with any projector on the market. UST or standard throw.

Now, my questions would be about whether this is an add-on to an existing space, or whether you are building this space new or what is going on?

I would think that if you are spending the type of money which a Stewart ($$$$) screen costs and looking at a NX7 ($$$$) which are really designed for very nice dedicated home theater spaces, that you are working with a budget that might be better allocated to installing the proper cabling and system in place from the start for a traditional setup.

I'm not sure of the layout, but a projector like the Epson 5050 is a good deal nicer than any of the UST projectors in terms of image quality, and not nearly in the price class of the NX7. It is solidly bright and delivers a very satisfying image for an outdoor environment which won't ever be as controlled as what a dedicated theater would be.

It offers a nice step up in terms of quality compared to the Epson 3800 which is bright, but misses out on the black levels (contrast).

If you actually are cinema enthusiasts, then it really seems that you are doing yourselves a major disservice by not being quite serious about the audio. Take a fair bit of that projector budget, and install good speakers in the space, in the right locations that can deliver the sound quality a decent setup deserves. It won't ever be 'great' when it is outside, but it should never be the thin sound of an integrated speaker within a projector.

Smart features are what you can buy for $50 or so from a Roku or AppleTV. So that's hardly a real consideration. Just something to be aware of. Keep in mind that projectors are notoriously behind the times as well when it comes to smart integration. So, if your Samsung TV or Sony TV is awesome, don't expect the same from Optoma. Even Samsung will be behind their other Smart products with their projectors. It's really quite sad. Just get a Roku. But, pair that Roku with a proper surround sound receiver and a universal remote that works outside with your electronics inside.

A standard throw projector is much easier to setup as well if you are moving it from outside to inside. It may not seem like it, but a UST projector is FAR MORE picky about placement. A long throw projector uses much smaller angles. So, if you are off by a few degrees, it may make a few inches of difference on screen, but a projector with lens shift like the Epson 5050 can correct for that easily.

UST does not have lens shift. You have to place it perfectly, every single time. This is fine for a white wall, but when you are aiming for a screen, you have to get it dead on. Half a degree difference can make several inches of difference on screen. A half inch forward or backwards? Same thing.

UST projectors are ideal for those using a white wall who want the 'big screen' experience in a room that has no other options. But, you give up contrast, you give up sharpness, and you give up image uniformity for not having to run wiring where it needs to go. That may save you a few bucks, but you are giving up a lot.

Then if you get a ALR screen, you end up giving up a fair bit more.

That is extremely valuable insight, thank you! I've attached a photo of our potential theater space in the back yard with prior screen set up. Our plan was indeed to mount a retractable Stewart Oasis (outdoor rated) screen to the rear of a rectangular water feature (debating between leaving it outside vs putting it up with each use, leaning towards the latter.) So with a retractable screen set up - and utilizing a smart feature like a Roku - it sounds like a standard throw projector makes more sense for an outdoor space. For outdoor, it still should be an ALR screen, though, correct?

As far as audio goes, we were investigating a landscape audio system but the actual set up remains a bit unclear to me. I was thinking of housing a dedicated amp in the adjacent grill space, and then presumably would have to run some type of audio input wire and house it in a waterproof enclosure, such that it is long enough to reach into the grass where the projector would sit. Our WiFi signal reaches 40-50 mbps in that area, so, other than the audio input, I assume we would only need to account for an extension cord to power the projector.

The JVC NX-7 was simply recommended to us, but we're certainly very much open to more cost effective options. Will definitely look into the options you mentioned. If you have any other suggestions based on the photo, I'm open to it.

Thank you much!