Hi Morgan; Big Welcome to Permies!
A little more information about your system would help.
You mention 2 inverters? Why two?
Do you have any charge control hooked up to protect the battery?
What type and size battery are you using? How are you monitoring it? Just a voltage reading? Do you check the battery itself? Water level, specific gravity of the cells?
As you discovered, any electric heating device will run down your battery.
Bigger or more battery's would delay that. But a heating element is a hard draw and should only be used sparingly.
Sounds like you are wanting to create and use your solar energy when you can and use utility power when the sun is not shining?
A 100 watt system just can not do very many things.
500-1000 -2000 watt systems can run bunches more things, but it comes at a cost.
Bigger better battery's, large charge control, pure sine wave inverter's ... the list goes on.
To use what you have, turn on more things when the sun shines.
Lights, stereo, fans, TV ...
Just monitor the battery and turn them off when your using too much power.