Just saw this. There is one and only one solution for you as far as I know. PROBE wetsuits. Google search them. They are made in Australia but they have a great website, they respond very quickly to questions, and shipping to the states is fast and very reasonable. You want the "iDry" models. They have every option you want, from 3 mil fullsuits to 9 mil farmer johns. They use a hydrophobic fleece lining. I don't know what the magic is, but if you turn the suit inside out and give it a good shake, the lining is 95% dry instantly! Hang it for 10 minutes and it is completely dry on the inside. The outside neoprene, of course, stays wet like all wetsuits because it has the standard nylon coating (which also preserves abrasion resistance, UV resistance, etc). But, you are putting on a dry and warm suit, on the inside. There is a video on their site that shows this.
I have some of their "frogskins" dive skins with the same lining for my winter outdoor pool workouts, and, yes, they work exactly as advertised. The fleece really traps water and also is very warm in the air. In fact, you could unzip the suit, shake it out to dry it, and zip it back up and be pretty warm. There is a still evaporative cooling from the outer layer, but the key is that it does not transfer to the dry lining anywhere near like a wetsuit that stays wet inside and outside. If you added a parka on top you would be really warm.
I am losing some weight now, but when I get where I want to be, I am getting their 5 mil for my Florida winter diving. I wish I had one for my recent trip to Cuba where I was doing 4 dives a day. The price is less than your budget, including adding a hood, gloves and boots.