I wouldn't worry about it to be honest, its not so much the water content that causes bad taste but wet sap, I aint so shore that many people think the same as me , what is the water content of the meat we cook ? water is tasteless and odorless minerals may add some taste, if the sap is down in the fall it don't take a lot of seasoning , water pans don't hurt flavor so why would water in wood taste bad? lot of myths and 1/2 truths in a lot of stuff out there imo
You have a very well balanced fire. Charcoal and wood are the best of both worlds, and it makes it easier to maintain.
I've never watched splits enough to see if they weep moisture. But... moisture content is really important for flavor. I buy wood that has 15% moisture, this is not green by any means, but when you smell the chunks or splits it smells like wood. Having some green is fine and you can sneak it in to an established fire and get some great flavor. You probably figured out that the biggest cost of using a stick burner is wood (and labor for ash removal). Consider investing in a $100 moisture meter, and buying wood three times a year. I buy my chunks three times annually, and always have good quality to draw from.
my wood is stored outside in a 20' long x 3' tall rack with 24" tin roof. well seasoned but if it has been very humid for extended days or long soaking rains it will absorb some moisture and looks just like what you seeing. never a problem.
All wood has water. As long as you're starting it on a bed of prior embers, I don't see a downside to wet wood. A little temporary steam? Heck I like water pans for continuous steam.
Now if the wood has mildew/mold, well that's another thing.
You want wood with 155/20% (max) moisture content.
It makes a difference in how hot the fire burns and how quickly and hot the coal base runs.
Buy a moisture meter off Amazon for around $30 and use it before you buy wood.
A few years a go I bought less than properly seasoned wood from three different sellers and the great easy to tend fires I was used to went out the window and it took me a while to figure out that the sellers "fully seasoned" wood was 40% moisture.
That was $300 worth of worthless split wood.
Three years later it was down to !8%/20% but by that time the rats spiders and wood roaches had moved in and the wife made me dispose of ALL of it.
And yes it was stored on a metal rack off the ground and under a proper zip up cover.
I saw an Aaron Franklin video on You tube a while ago, and he said he uses green wood all the time. I have tried it a few times myself, from an oak tree in my backyard & if you have an established fire it burns just fine. Can’t add too much though, cause it does give off a bit more smoke.
Visually, steam and smoke can be easily confused. Still, steam helps smoke stick to meat better. So if you want less smoke flavor, you probably want drier wood...or just use less wood and more charcoal/gas/electricity as a heat source.
I don't like wet wood because even if you have a fire hot enough to cook off the moisture, it's a lot of lost heat, which means increased fuel consumption, and usually it causes temp swings. The burning wood "stalls" while the moisture cooks off, then burns up FAST. You get lagging temps at first, then a spike. Set it aside for 6-12 months and have a nice hot clean burning fire when it's dry.