Drywall – How to cover large gaps in drywall

You indicate that you have been in a drought since October. Combine cooler weather, better insulated roof, and heat being on; the structural framing of the house may have shrunk.
I experience some "seasonal" cracking and shrinkage in my home. See what it looks like in July/August, if the condition persists, consult a local experienced contractor.

Option 3 is the sanest IMHO. You can get a bucket of drywall mud for $15 and do a "skim coat" over the panels to create a flat surface. No need to sand first; this stuff will stick to anything! Once the mud is dry, you can sand it to get a smooth look, or texture it. Texturing can be done with cans of spray-on texture you get at big box stores, or using a texture sprayer gun. A pro will be able to do the texture part much better than a novice, so if you want a textured wall, I recommend hiring that part out for $100 or so. With the right equipment and an operator of moderate skill, it's a 30 minute job. If you've already got an air compressor, you can have a go yourself with a sprayer attachment that has a hopper.

But whatever you do, match the texture or lack thereof to any drywall that abuts the paneled wall. Nothing screams "I used to be wood paneling!!!!!" like strange, awkward texture on a few walls that, upon further investigation, have more give to them when pushed on.

This is the approach I took on my wood paneled walls and today you'd never know the difference.