True, you do not want to cover recessed lighting with fan blades unless you like the strobe effect. In some ways I'd prefer two fans as it will cover more than one, and give the option of running just one. Let's remember that fans don't actually 'cool' a room, they move air around, and make us feel cooler from evaporation (I've seen people switch on a fan and leave the room for it to 'cool down' lol) Keep in mind the option of some sort of roof vent and/or ventilating skylight, that would be very effective in the evening.

I also fretted about putting a ceiling fan in a room with an 8' ceiling but went ahead and did it and I don't regret it. I put 2, in 2 bedrooms with 8' ceilings, low profile models from Hunter which I think are discontinued. They have 3 speeds, the slowest of which is silent but useless. The 2 higher speeds make a bit of sound, a pulsing humm, in addition to the sound of air being pushed around, the latter to be expected. I put very beefy supports for the fan in the ceiling and I put additonal rubber padding between the ceiling and fann connections to further eliminate any vibration noise. But, that electrical pulsing humm is there. I figure it's a cheap electrical motor in the fan, and maybe getting a better fan would be a good idea. I paid about 200 bucks per fan. They have remote controls, which are nice when you wake up freezing in the middle of the night and all you have to do is reach for the remote on the nightstand to turn it off. Making the bed requires a bit more consideration but the room doesn't feel closed in to me.

What is there now is just plain tacky , the fan and all that lighting needs to go. As for pot lights they are a great thing for one level of lighting but IMO cannot be the sole source of light in a room. I agree to add the insulation between the beams an close them in with drywall that will give you the opportunity to add 4” LED pot lights and then if you want you could add a couple of hanging lights too. But you need to add lamps for a good level of light lower in the space.

We have a fairly modern design (with big ceilings in a great room). Went with a pretty modern fan.