I read your post a couple times before considering a response. This is a free opinion, and, in spite of your self-described stubbornness, I offer it with friendly sincerity.
Make this first trip out
easy - leave the kayaks at home. The SUP should be easy enough for the two of you to put on top. I have seen plenty of the big houseboats on Lake Powell towing a bunch of stuff behind them (a bow rider or wake boat, and several jet skis)... usually rentals. They don't have as much concern about fouling a line in the prop - a real concern in your situation.
Lake Powell is a spectacular place, and you will have no problem finding great places to explore with your boat. The C-Dory can get into places deeper draft boats can't, and you can beach it. Make sure you have an easy way of getting back on the boat - we went bow to the beach and used a two-step step ladder to get back onboard.
It is going to be hot at Lake Powell, so you will want to get into the water to cool off. Look for places where you will have afternoon shade to beach for the night. Be aware that the mass of other boats on the lake will be looking for the same.
With that in mind, even in this usual time, I would expect plenty of boat traffic. If you are towing two kayaks, that is more to deal with, with the regular wake you will experience.
I am not aware of the premise of towing from a forward cleat with the C-Dory, unless you are talking about hip towing (towing alongside); generally used when in tight spaces or a lot of other boat traffic, as in a marina). If you are determined to tow the kayaks, I would use polypropylene line - it floats. Add a couple in-line floats (as used on lines in swimming pools) where the line is in proximity to your motor; keeping in mind that the line will collect there as you slow down. Depending on the design lines of your kayaks, they may try to get airborne or submarine if you tow at speed... you will need to experiment with line length to see where they tow the best. At night, when beached, I would keep the kayaks tied right alongside. If you intend to back to the beach, you will need the kayaks out of the way.
From what I'm writing, it would be more to deal with than I'd care for (the reason we kept the kayaks or dinghy on top when underway) to tow the kayaks, especially on your first outing.
Another thought: pick up an inflatable tandem kayak, like a SeaEagle.
https://www.seaeagle.com/inflatable-kayaks
Easier to put that on top when underway on the water. Or, deflate it and stash that in the cockpit.
This first outing will set the tone on your future boating experiences. I'd suggest keeping it simple while you learn the functions and handling of your C-Dory.
Lake Powell is a special place. It can also be a very busy place between Memorial Day and Labor Day. The experience you have there at this time will be very different from exploring the lake in the spring and fall. I wish you all the best with this first outing.