Yessss for a "third" in agreement.Just my 2 cents, and someone else can jump in if they disagree, I would get rid of the half log or at a minimum block off one end of it so there's one one entry/exit. BPs like secure, size appropriate hides and having something open on both ends could cause some stress to your snake. I'd also block off three sides of the enclosure so your BP feels a little more secure, and I can't see if you have a second hide on the cool side, but would put one in if not. If you can get some foam or some other type of insulating material for the sides and back of your enclosure, it will hold heat better and your heating elements won't need to run as much, thereby reducing the drying effect they're having on your enclosure.
The humidity being lower on the warm end is perfectly normal. Even in my enclosure now that's highly modified my warm end is 55% and cool end is 65%. Personally I've always kept my humidity somewhere between 50-60% and have had no issues, because I have a humid hide that's upwards of 70-75% that's available 24-7 for my BP to go into if he needs it. I also mist once or twice a day when in shed just to be safe.
Don't get too hung up on humidity. Different sites will tell you different things, for example, the Reddit BP section moderators will tell you that 80% is ideal and that anything lower than 60% is dangerous for a BP, which is just.. not correct. I would focus on some of your other enclosure issues first.All of the above.