Do you have an assumable mortgage? Is it at a lower rate than a buyer can get today (probably not - interest rates are still pretty low, unless you bought your rate down when you purchased)? If your current mortgage cannot be assumed, and isn't more attractive than a new mortgage, then finding someone to take it on isn't likely.
I'm curious what the stressful part is for you? Some people do need to move out of their home in order for us to sell it. But, most often, the times I've run into that have been because someone was chronically ill and unable to keep the house staged and show-ready. If you need to stay with friends or relatives until it sells, you would not be alone. Lots of people do that. Move out, put your things in storage, and put the home on the market while you live somewhere else. But, be sure you price the home to sell, as you can wear out your welcome if the home takes a while to sell.
There are still home builders willing to take contingent offers. That means they'll accept your contract for a new home to be built, while you are selling your current home. It's not a trade, but it's a way to trade-up, knowing it will take 5-6 months to build the new home, during which the current home can be listed and sold.