That dampness is condensation from your own breath, and once nights get cold it gets way worse no matter how many vents you crack. Two people breathing all night put out a surprising amount of moisture, and it rises, hits the cold shell of the tent, and turns into water right where you're sleeping. That's why the head end is soaked, that's where the fabric is closest to the roof and gets coldest. Cracking the rear window helps a little but warm air barely moves on its own, you need actual airflow pushing the moist air out.
A battery fan genuinely does make a difference, it's not wishful thinking. You don't need something huge, just enough to move air across the tent. The trick is placement. Point it so it creates a flow from a low intake point up and out through a vent near the head end, since that's where the moisture is pooling. I run a small rechargeable one all night in mine and the difference between fan-on and fan-off nights is night and day. Wake up and the fabric is just cool instead of dripping. Other things that helped me. Sleep with a window cracked at the opposite end from your vents so air actually travels through instead of just swirling. Pull the mattress out and stand it on its side when you're not in the tent, a damp mattress sandwiched between fabric layers never dries. And if your pillow is getting wet, throw a towel under it and just accept you'll dry the towel at camp, or use one of the thin synthetic pillows instead of a plush one that holds moisture.
On the packing question, you don't need to leave the whole tent open for hours. What I do is pop the top, pull the mattress out to stand upright, wipe down any wet fabric with the towel, and leave it open while I make coffee and break down camp. Twenty to thirty minutes of sun and breeze on the mattress does most of the work. If I'm packing up damp beacuse of rain, I'll pop it open again that evening at home or at the next camp rather than letting it sit closed for days, because a tent stored wet is how you get mildew and that smell never leaves.