Electrical – use a 70 amp panel for a 30 amp service feed

Each baseboard heater is probably 15A (if not then check what they actually are), and the dryer is 30A. So you're already at 90A. The washer (is it frontloading?) will need 15A/2 (it's 120V), and so will the bathroom, so that's 105A. I can easily imagine all those running at once. Then you have some plugs and whatnot, but you probably won't max all of them at once.

Looks like 120A will be OK, but just barely. Is electrical heat really your only option? Can you use a gas dryer?

What @Harper said. The problem we have have with a question like yours is that we could say "yes you could update it" but we really don't know is what kind of loads you are applying at the end of a circuit. We are guessing that it is greater than 30A because you want to upgrade. Also you give us a distance of 300' which is a substantial distance so voltage drop will surely come into play.

For example if your load is 40A at 240V which would be 9.2KVA then at a 3% Voltage Drop. Then you could run 333' with a #4. A #6 would only be good for 210'. If you load were 45A or 10.35KVA the distance with a #6 would be no longer than 186', A #4 would get you 296' so technically you would need a #3. Buy the way this is all in copper.

So you need to get distances and loads for the pump either in HP or KVA and voltage requirements and a demand load for the rv either in Amps or KVA and operating voltage. Then there could be a more complete and informed answer.