Apparently the Meateater has spurred a lot of interest. Honestly, guys around here don't get too excited about them.
They've been hunted in four counties in MD (Dorchester, Worchester, Wicomico, Somerset) for 40 years or more. Those counties have also produced some of MD's bigger whitetails. So the lease rates are fairly high. The lease rates are undoubtedly driven by the whitetails, and not the sika deer.
Your best public land options are the Blackwater NWR in MD, or the Chincoteague NWR in VA. You'll need to draw a permit, but they aren't hard to draw. The hunts are marginal. I've only bowhunted them but you're hoping for them to move in the first 30 minutes and last 30 minutes of each day. This is true even during the rut (mid-late October). They simply don't move at any other time of the day. Gun hunters often try to flush them and shoot them as they run away, at least at Chincoteague.
I shot a 1-1/2 year old doe and she weighed 18# field dressed. My buddy shot one of the largest bucks taken that year. It weighed 54# field dressed. At Chincoteague they weighed every one and the weights ranged from 8 to 54 the last time I checked, which was about 2014.
The mosquitoes, at least in October, are "next level". Wait, no, they're not "next level", they are simply not of this world. Honestly, if you think you've seen mosquitoes before, you haven't. They are simply amazing in the swamps. You will breathe them in. You will need two thermacells, at least, per person, and you'll still get a lot of bites. The FWS collects and studies the mosquitoes. I don't have any idea why.