I think you're 100% right on in terms of your storage plans.
Too many times I've seen folks go out and spend a bunch of money on a 50 or 100-count desktop humidor, fill it up, buy another one, fill it up, and then buy another one before realizing that they've invested so much money in several small storage spaces that all need separate maintainance, when they could have gotten a good sized cooler for far less and used that cash to fill it with some primo stuff.
The reason people have done the cedar lining is to have a buffer of sorts, so that the wood can absorb and release some humidity, keeping things from wildly swinging up and down each time you peek inside.
Open air is your enemy in this regard.
Just starting out, my advice is to pack it full of empty cigar boxes from your local shop. Some places charge a buck or two, some just hand them out to anyone who asks nicely. either way it's cheaper than buying spanish cedar in sheets and trying to cut them down to fit your cooler. (The dust is toxic if inhaled, so if you do decide to go that route, be very careful and wear protective stuff).
As for me, I went to Sam's Club and bought the biggest cooler they sold. It had gooves built into the insides, so I stood it up on end and put those cheap white wire closet racks in the grooves to act as shelves. Since I had more empty boxes than cigars at the time, I enjoyed having the space to organize my singles in boxes by date, brand, or whatever. A luxury I miss, and I've had to give myself a "No OCD Rule" when it comes to organizing my humi.
So your cooler is "full", your beads will humidify without fail, and the cooler will offer you a fantastic seal and worry-free storage.