I agree with others that that it's better to rough turn sooner than later.
If it's too humid for Anchorseal to dry on your blanks, you will probably see the same issue on rough turned bowls. You could likely skip using Anchorseal on the bowls. But it seems like everyone's drying situation is different so you will need to figure out what works for you.
I turn quite a bit of cherry. What I've found to work on
rough turnings is to coat any remaining sapwood with Anchorseal. I don't coat heartwood. Let the Anchorseal dry overnight. Then store the rough turned bowl in a paper bag, then inside a 2nd paper bag on a wire shelf so there is even airflow around the outer bag. For the first week or so, the inner bag gets moist, so I'll change that out every couple of days until the bag stays dry.
Inspect the bowl occasionally looking for cracks which are most likely to occur on the outside, starting at the center bottom (tenon area) or in any remaining sapwood. If you see cracks, drip some thin CA glue in them to stop the spreading, and mark the end of the crack with a Sharpie marker so you can see if the crack is growing next time you inspect.
Weigh the bowl occasionally to see how it's drying. When it's losing weight slowly, stop using the paper bags. I have a sickness that causes me to like doing mental arithmetic, so when I see the bowl is losing less than 1% of its weight per day, I stop using bags.
All the above is for rough turned bowls, with wall thickness roughly 10% of the bowl diameter. Most of what I make now is natural edge bowls that are turned to final thickness (3/8" or so) right away. For those, I just put in paper bags, never use Anchorseal. If you hope to preserve the white sapwood that Hockenberry mentioned, it's important to change from damp to dry bag frequently. Some people also spray with bleach or other mold preventing solutions to stop discoloration. I don't have any experience with that.
Also, the above is for the black cherry we have growing in the wild in Michigan (
https://en.wikipedia.org/wiki/Prunus_serotina ) Not sure it applies to the wood you found.
Good luck
Dave