Have pretty much solved the issue by using the down coat. I picked up one with the highest "fill power" I could afford. Depending on indoor temperature, I can either wear the coat over just a standard t-shirt or over the shirt and a fleece vest. If I'm still cold, then I will wear a long sleeved fleece shirt over the t. I don't experience any discomfort with this set up. So far, no sweating either.
I can still switch out to the electric coat but only if temperatures reach 55 F or higher. I don't seem to end up feeling "wet" then. I still don't know the reason for the feeling, so that remains a mystery. It could be that the electric coat elements don't provide even heating to my body, causing small areas of hot and cold spots right near each other giving me the feeling. Maybe when environmental temperatures increase and there is less temperature difference between the spots, it's not enough for me to get the wet feeling.
Yes, I have an electric blanket I use at home too. The blanket itself is fleece and I usually use a fleece blanket cover. What I set it at before bed depend on what I have eaten during the day as well as the house temperature. With the Covid crisis, sometimes food doesn't arrive here in time and I eat very little for several days, just some pasta for quick energy and that's about it. By night, the pasta benefit has often worn off. Then, even with the electric blanket on and set where I normally would set it, I still end up with chills during the night. At first, I thought my blanket was going bad because, say just the day before when I ate normally, the same setting just wouldn't do the job! Never realized how much of a difference food could make with overnight warmth! However, I now do have a down throw I can use over top of the electric blanket should I encounter chills again. Works great and I usually don't need to run the blanket after a warm up period, but the down retains the heat so well that I can't use it if I'm eating normally or I wake up in a sweat, which is something I absolutely hate! Fortunately, as I've been learning about my body and the temperature, this doesn't happen often.
A few years back, I tried only a down blanket scheme at home for overnight warmth. I used two layered blankets with as much fill power as I could afford. They ended up thick and I felt like I was sleeping within clouds! However, even if the house temp dropped into the mid to upper 40's, I would still wake up sweaty and that was with a fan aimed towards me running at middle speed! So that bed was abandoned and the comforters are still on it. I suppose if a crisis ever hit where temps dropped to outdoor temperatures, that set up could come in handy.
Oh well, this whole thing has been an interesting learning experience for sure.