Passive solar greenhouse, angle of south facing "front" at my long-lat

Hey Permies Peeps.

I'm meeting with a builder to see if they will (help) build my passive solar greenhouse. I'm trying for a 26x54-ish footprint, more-or-less lean-to, north portion half underground, and tall enough to let a banana bear fruit whenever it wants to. I'm math challenged (being a wordsmith more than a numbers gal), and am NOT confident that my guesstimate at a "30-degree slope aught to work just fine" is correct here on my little chunk of NC. I plan to us double wall polycarb for all glazing, plus windows that open on the south vertical wall, and one or two each on the E and W walls, where they are above grade (yeah, duh). Plus at least one thermostatically activated vent fan (at peak on the N wall? W wall? E wall?), or more if the FarmTek guys can convince me I need more. Do I need an evaporative cooler? My 14x50 caterpillar tunnel is a sauna 8 months of the year, and kept my in-ground turmeric safe all winter, even through the big freeze in February (one end of the tunnel is still wide open, btw). So ... I'm running a half-way farm. Everything is halfway finished or halfway fixed. I just don't want it to be half correct on something this big that I'm investing a lot of time and money in.

Location specs: zone 7b, long-lat is 35° 51' 43" N, 80° 32' 40" W (35.862110, -80.544574) according to https://www.mappr.co/latitude-longitude-finder/.

I gleaned the images in the attached file from a sun path site, calculated at the solstices (should I have looked at equinoxes?) to see the variance ... and from that guessed my S-facing sloped roof glazing should be around 30-degrees. Is this close? How should I have calculated it?  Should my non-glazed area at the top of the roof be more than 6'? Less? I don't want to be dragging shade cloth around the structure's roof during the July-Aug heat wave next year ...

Sorry to seem to naive on this. I know I have a lot to learn, so I'm hoping someone out there can help me with some shortcuts so I don't spend money I don't need to, or do a poor job with planning and negate the great benefits that passive solar allows! And I'm sure there are questions I should be asking that I just don't know I need to ask. Please help!

Looking forward to hearing back ...
Felicia