Whatever you do now, it will cost more than your current mortgage. If you are looking to pay off such small things, you have to take into account the extra cost on that whole mortgage. A 30 year fixed for $201,600 (80% of your financed house) is a $850/mo payment. The same thing at 5% is $1,082. Over a 30 year life, that would be $84,000 more in interest. How does that compare to what these current debts are racking up?
So, the first cut MMM advice should hold--cash flow your debts.
If you were going to *invest* a good chunk of your new house, you might get some supporters. But interest rates are going up, cash refi rates are above the public standard rate, and HELOCs are floating, so they will continue to go up for the near term. Meanwhile, the stock market isn't looking its healthiest; with high inflation, returns aren't likely too be too good, either, in a similar timeframe.
Might it work out? Sure. You probably won't hold the mortgage for a full 30, either. But you are taking a gamble doing this now. It might cost you quite a bit, particularly if the worse elements of the economy persist for some time.
Why didn't you do it last year? Would have been a better time. If you don't know the answer, then you might be suffering a bit of FOMO, like the buyers still in the housing market at the moment.