Our shop areas are close to the same size then.
Mine is a Gree. I'd never heard of the brand before this, but turns out they are the largest producer of mini splits in the world and have an excellent track record. It's been running around the clock for almost 5 years trouble free now... It only raised my bill $30-$60 a month depending on the season (small price to pay to stay comfortable and humidity free IMO.) Not to mention I have a 14x40 lathe in the shop and I wanted to protect that investment.
Yah, down here (Alabama) we have humidity in wintertime as well. I ran my propane heater most of the day Saturday amd noticed it was starting to ice up.
I'll look I to that brand (Gree) . I plan to do the office first.
It might be worth looking at a multi-zone unit in your case(?).
I'm in upstate SC, so lots of humidity here as well although winters probably aren't as humid as in AL.
Since I can't really compare apples to apples here with our different building methods, just let me say the split works awesome in my situation. As long as you have decent insulation I think you would be fine. I don't set temps the same as I do in the house, i.e. the shop is 67F on heat and 74-75F on AC, which keeps it comfortable and dry. I have no insulation whatsoever, but I did make good use of radiant barrier (RB) for the roof, and structure ends. The soffits are connected to the roof vent by way of formed plenums from the RB on the bottoms of the truss risers.