Serendipitously, I own a Gatewood cape; I started the AT with one but swapped out due to a lot of blowdowns at the start.
I've read differing opinions on this, but I'm 5'9" (I swear I used to be 5'10" but at my latest physical, the nurse said ...), and the inside feels pretty tight to
me in order to keep the end of my sleeping bag from touching the tent fabric. Though note that I use a size regular neo-air, which sort of pushes you up enough higher as to make a little difference there.
In the so-called "desert" you can probably make one work even at 6'3" as you won't have condensation to worry about. In your shoes I'd just go with something like a Golite poncho, but in fact it is more of a challenge at your height. There's just more of you to cover! If possible, see if you can borrow a full-length type of poncho and practice setting it up different ways (grope the internet for setup pictures/ideas) and see how vulnerable you feel under there.
Or, of course, just get a lightweight shelter that fits you and carry it for the whole trip.
Given that you're likely to have little in the way of rain to deal with, I'd think in terms of a sort of minimally acceptable rain coverage starting out, knowing that (a) I can tough out one or two uncomfortable nights for substantial weight saving, and (b) things dry out so much faster/easier in a dry climate. But it certainly can pour out there; it didn't for me, but you might not be as fortunate.
"Would you set up your tarp in the desert if it started raining in the middle of the night, or literally just pull it over you?"
It's situational. If chance of rain looks really low (the normal state of affairs in the first 700 miles), I'd just have the poncho or tarp or whatever in easy reach, know where it is. Maybe make sure the DWR on your sleeping bag isn't worn off.
If in the night it started raining with any sort of volume and sustainability, I definitely would pitch the shelter rather than just pull the fabric over me. It's more just if a few drops are sprinkling I might not bother, you just make a best guess.
If in the evening the clouds look at all threatening or if you have a weather forecast that suggests any risk, set up the tarp before you sleep.
Weather forecast: btw, cell reception was in general better in southern part of CA than anywhere else on the PCT, so if you have a smartphone or happen to be hiking with someone that does ... it's not at all unreasonable to check the weather forecast when somewhere on relatively high ground.
"The MLD supermid is just that for me and my cousin, but what would be a good solo alternative? Again, I am a big, tall guy, and I like to have a little extra space."
I used a tarptent contrail from Kennedy Meadows onward, and I found that to be an excellent choice, and it would be so for someone much taller too. It's a lightweight and spacious solo shelter, single walled.
For a tall person looking today, if you use two trekking poles, also have a look at the lightheart designs "solong" --- a tent variant designed for tall people. I used their cuben solo (standard, not "solong") on the CDT last year and loved it, it's nicely designed.
I have no experience with that MLD or with pyramid's in general. You might camp a night or two in places where it's very windy (and thus where the extra stability could be good), but that will be the rare exception.
One possible downside with a big tent like this as a solo shelter is finding tent sites. Not much of a downside for most of the PCT, overall in CA I found it easy to find places to camp, but in WA state we've got lots of brush growing anywhere there aren't trees, so often you're looking for pre-existing cleared tent sites in the latter part of your trip, and the time when you'll most need something more out of your tent than bug protection.
All that said, MLD makes great stuff and the supermid is pretty light, even if you add in perimeter bug netting.
Perhaps if you post (or just search) on BPL (backpackinglight.com) you can get some good reviews from folks with pyramid tent experience.