How much money ya got? Louvered roofing can be adjusted to block the neighbors view, but not the sky.
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You could simulate the adjustable ones with a fixed wooden or vinyl or metal louver material, that wasn't adjustable, for significantly less cost, especially if you built it yourself.
We could easily do pretty much whatever we wanted for this, but the real question is how much we want to spend of course, not how much we have.
At a local hot tub store we saw the
Covana Oasis on display on a filled hot tub inside the store. I have to say, it was tempting and I still think about it. Very well insulated lid/roof that sits on the spa with a air tight seal, which would minimize heating costs. When you want to use the tub you twist a key and it rises up, making a gazebo over the spa, with color selectable lights. There are privacy screens on three sides that can either be lowered as desired or left attached, in which case they automatically extend when the roof is lifted. Despite being $7000, it was, and is, very tempting. But I’m not sure if I would like a permanent roof overhead or not. On the flip side it would give use the privacy we want, and would be a much better shelter for rainy days than the umbrella the previous owners left that can be extended over the spa. That works well for rain with no wind, but wind will push rain into the spa.
Tradeoffs for everything I suppose...
The angles are fairly low, I think a 6’ privacy fence or similar next to the patio would block the line of sight from the neighbors house. And would be cheap. The question is overall looks vs functionality I suppose. That’s why I wanted ideas, often someone has an idea you never thought of (like rotating the hot tub).
Ooh, I can't officially recommend not getting a permit, but I wouldn't voluntarily invite an inspector into my house or yard. Where I used to live, they were mandated to look for violations, and not limited to the permitted project (city/county revenue source). Plus, an inspection doesn't always guarantee the job is done right, or even to code. A lot of inspectors are retired and/or failed contractors. Need I say more? Better to spend your money on a qualified local electrician. The right one will do the job right, to local code, and mind his own business. Some municipalities would not even require an inspection for such a project. Just some things to think through...
Electricians are required to pull a permit, and all electrical or pool/spa permits require an inspection or two. I understand what you are saying, though in this case I wouldn’t expect issues as I’ve had an inspector here for my pool site inspection before I put that up, and when my electrical service was upgraded (which I hired an electrician to do) the inspector came out for that. While he was here he did the required final inspection for my pool. So if there had been issues they almost certainly would have been raised before now.
That said when I emailed the inspector with a couple questions before I put my pool up, he asked who was doing the electrical install and when I said the company, he said “they know what they are doing.” So it’s entirely possible the degree to which they inspect for issues depends on who does the actual work. DIY is allowed for homeowners per local code if you take and pass a knowledge test before you do your work, but they probably inspect it a lot harder than they do the work of the company I hired earlier this year...
. I have never noticed it really mattering which way its positioned so long as when its 1/2 open i can access the control panel. My motto is try the cheapest, simplest method 1st before getting too complex. Hope it works out as envisioned 
if not just start skinny dipping- they’ll probably start looking away or build their own screen lol