1. "Can anyone else offer their perspective on camping in the rain (with this tent or any other tent)?"
I now trek only in Colorado and northern New England (reasons for that are another story). In NNE, rain may go for days, but there are regular periods where the rain abates a bit. Plus there are lots of conifers that provide further shelter. So I just wait till the rain lets up a bit, and then get the tent up. Ditto for nighttime exits in my undies wearing the rain top if needed over a fleece top and cap, and neoprene divers sox. Burrrr!
In Colorado, the rainstorms are usually short, but sometimes they can be very strong all afternoon and night. These are the challenging times you raise in your post.
One approach is to bring a light cuben tarp that can be strung between tent poles or trees, and use it for cooking and eating. This approach won't work, though, in a real blow. For this and other reasons, finding a protected site is a key to camping in the rain. If too far above timberline to do so, you should have planned better, and may have to eat cold food, as you intimated.
A small chair is also great to get off the ground and relax for dinner.
I use only dome tents, partly because they provide plenty of space to move around under cover so I don't get wet rubbing up against the tent walls. Still, as already noted, the size of the vestibule is a key to rain management. My last tent had awnings, rather than closed vestibules, at front and back. I camped only in protected areas, and for the first time, enjoyed cooking and eating in heavy rain, with the gear stored under the rear awning and not in the way. Sat and cooked in the chair in the tent, looking out at the downpour, but did have to keep my feet from sticking out from under the front awning. Never tried this in areas where bear visits are prevalent, and don't intend to. (How do you know if you're in such an area? That's another story, also.)
The current tent has a good, but average size vestibule, not enough for my former routine, but needed something that would totally button up for camping in open places. So, I'm working on a tent now that has the best of both worlds, with a front awning that locks down into a closed vestibule for blown rain. Still won't be able to cook comfortably in a real blow, though, without the awning.
With a good tent, I find the pounding or pattering of rain, as the case may be, to be comforting, and it puts me right to sleep. It may depend on the quality of the tent. If you don't trust it, especially if it shakes around and spatters moisture on you, the pounding could be nerve wracking. That's another reason I like good quality domes - very stable.
2. "I'm still wondering about entering/exiting strategies and where to store wet gear, if the tent doesn't have a big vestibule. (It seems like having a big vestibule is a huge advantage of the TT Rainshadow... but I'm confused why it seems like no one talks about vestibules in general"
As you point out, next to inner space, the larger vestibule is the key. A second vestibule is ideal for wet gear. Under the rear cover, I put the boots next to the floor wall, then the folded mesh chair, then lay the pack on the chair, then spread the rain top over the pack where it will dry a bit.
But you also need a good size door in the outer tent that is large enough to pass through without getting wet, and most important, extends over the perimeter of the inner tent so rain will not fall inside.
And you need a tent that sets up without allowing rain to pour onto the bathtub floor.
I've gotten around this as mentioned, by waiting for the rain to let up a bit. But sometimes it doesn't. Got nailed only once in recent years, but it was no fun toweling out the bathtub floor, and my Sheltie was really PO'd. The solution can be as simple as a tent with DWR 'solid' inner with vertical mesh windows, that will keep the rain off the floor for the few minutes it takes to get it up and get the fly over it. With a single wall, or single/double hybrid, a design that pitches without exposing the floor is needed. Not too many light tents around like this, especially from the large companies.
By now, you may see why I make or mod my tents. What's for sale is either too heavy, too skimpy, or both. It would be good if tentmakers had to trek solo with their own products for at least a month every year (no llamas), preferably in the great North West. We'd have much more functional and lighter tents. But not gonna happen.
Many on BPL are using tarps, often of cuben, and often with bivy sacks, as is apparent from the posts and articles here. So naturally, vestibules don't enter into the picture for them. But for tenters like me, BPL is a great site, with lots of ideas for lighter and more functional tents, especially on the MYOG forum. It's a work in progress, so no one can direct you to the perfect tent. But if I didn't do my own, the TarpTent Rainbow solo or duo would probably be my tent, based on the considerations stated above. Although I liked the original Rainbow better with the zip up to the peak, and would probably put more tension on the floor corners, and make a dome-shaped netting inner for it, not for bugs, but to protect from the wet canopy. The Lightheart Gear tents look interesting, also; but I have no experience with them, or knowledge of how they compare to the SMD tents. The return of tent surveys to BPL would be a big help in this area.
Hope that's of some help to you, Anna.