Congrats on the new boat!! I'm using a Honda 2000i without any issues aside from reasonable limitations.
It looks like we have a couple of variables here that need some clarification. You have:
1) a 2000watt Hyundai Genny
2) You have an electric heater.
-> How are you connecting the genny to the heater? I have one of these (link below) which I plug into my Honda, then connect my shore power cord to the shore power receptical and use the breaker panel to control what is being powered by teh generator.
This requires some thought in regards to conservation. For example, I keep the fridge and the battery charger on all the time. However, I cannot keep the water heater on all the time. However, i don't really need to because it only takes about 20 min. for the water heater to heat the water and it holds heat for a good deal of time. I cannot run the water heater and the stove at the same time. I typically only run the heater and the fridge together with everything else turned off.
-> How large is the electric heater? How much does it draw? I use one of these and don't have any issues:
I can see that a larger electric heater could cause some issues.
-> The Hyundai specs actually look a bit better than the Honda
2200W Peak Power, 2000W Running Power
Output Current 16.6A, Max Circuit 20A
3.8HP 5500RPM 125CC Hyundai Motor
Two 120V 16.6A AC & One 12V 8.3A DC
120V 2000W max. (16.7A) 1600W rated (13.3A)
30A 125V Locking Plug, 20A 125 V receptacle
Fuel Tank Capacity
Run Time per Tankful
4hrs. @ rated load, 9.6 hrs. @ 1/4 load
Dimensions (L x W x H)
20.1" x 11.4" x 16.7"
59 dB @ rated load 53dB @ 1/4 load