Sounds like a somewhat similar situation to what I had to deal with and the solution ended up being simple and easy for me at the time because I didn't have flowering plants and the room my tent is in is small. I ran the humidifier right outside the open front door of the tent with an oscillating fan behind it blowing toward the plants. I had to run it like that about 20 hours a day for a few days and brought the RH of the whole room up basically. I only set the humidifier on a timer at night to go on/off every 30 minutes while I slept because I couldn't put enough water in it to steam all night. I had the tent wide open so I didn't need the exhaust fan at all.
You can also give the plants a nice dose of humidity by shutting the exhaust fan off and sealing up the tent all but enough to let your humidifier pump into the front door for a little while. Once you get a decent RH stabilized in the whole room and give it a blast like that, you can leave the fan off, pull the humidifier and totally seal up the tent for an hour. The walls will be wet when you open it up. Not recommended for flowering plants!
I don't know if something has changed here atmospherically but I haven't had to use the thing at all since my war with RH back in Fall '19. It's funny that once I figured it out and conquered it over the course of a few days, I haven't had to deal with it at all, my RH is usually between 42-48% and I can adjust it easily by opening the window to outside air for a bit. It hasn't gone down below ~ 38% in weeks. I actually just finally moved the humidifier/spatter tray out from in front of the tent yesterday because it's been so long since I've plugged it in.