Okay. Looks like a 6100 Heating Degree Day climate, averaging the last three years and assuming you keep it at 65° inside. Assuming the wood is actually dry, we can call it 25 million BTU/Cord. So, call it 6.7 cords, averaged over the same time, which is 162 million BTU, more or less.
If I got all that right, then 162 million BTU/1200 ft2/6100 HDD = 22 BTU/ft2/HDD. Now lower numbers are better, and generally, if the number is over 5, there are probably things to be done. The worst I've seen to date is 20. But here you are at 22. Now I could have gotten this wrong if you actually keep your house colder than 65°, but if you keep it colder with that consumption, then the house rates even worse.
Unless you live on a hill, I doubt you can fix a flooding problem with gutters. As you said: Evidently it's just groundwater.
So assuming you have a low efficiency woodstove and replaced it with a high efficiency natural gas furnace, you'd need 990 Therms of gas to heat the same house the same amount. Your current natural gas price is around 70 cents a therm, but I don't count on that staying level. Still, that means you'd pay $700 to heat your house if you went to gas, or maybe $800 if you have a lower efficiency system, plus whatever you might pay for system maintenance. This is cheap compared to Maine prices. Still...
You have a very leaky house. Close it up without really mitigating that water and you'll have a health situation from mold fumes.
I can't help but wonder if you can jack the whole thing up a few feet, fill the foundation with packed gravel, pour an insulated slab and above grade crawl space wall, and go from there. The thing is, this place is so leaky that a band-aid approach may not be economical.
I've got a decent summary of what else most houses need
here. Consider your options and good luck.