All of your symptoms seem to be a common group of problems.
A thick gasket between carb and intake will help with the heat... but it won't completely fix it. Modern fuel will tend to boil WAY before the old fuel did. I dropped my carb float level a bit. Less fuel in the bowl, less to bubble over the top. I also made a heat shield around the base of my carb. That also helped some.
Clogs in the lines are also a big problem. Short of replacing the tank, there will always be crap coming up from there. Filters up and down the line do help but the best fix is replacing the tank sending unit with one that has the filter screen at the tank pickup, or... add a screen to the pickup. Oddly enough there are bunches to choose from online. I fought with various electric fuel pumps swearing up and down that they were the problem. Turned out it was just crap and more crap coming from the tank. Mine was the original sending unit so there was no screen/filter at all. Who knew?
So drain the tank like EmTee suggested. If you can, drop it and really blow it out good. Add the screen to the sending unit (and I mean one of those supper fine sock thingies that fit exactly over the tube). Blow air through the whole system to make sure all is clear. Maybe toward the tank as anything stuck in the lines will dislodge going back the other direction. Make sure your fuel pump is really clean since you're really starting fresh. Install those plastic disposable see-through filters wherever you can. The glass screen filters look cool but they aren't as effective. Make sure you're clean, up to and including into the carb and you should be good.
One more thing. Make sure your exhaust butterfly valve (not sure what it's called but it's right below the carb) is working smoothly. If it's stuck closed or kinda closed, that will add extra heat to the carb and increase the vapor lock issue.