What do I do with this huge open space between my ceilings and the floor above?

Blown-in cellulose actually does fill a tall cavity like that, as long as the crew dense-packs it rather than just letting loose fill drop in. I had basicly the same setup in my old house, a couple feet of open space over the living room ceiling, and the crew ran a hose up thru the light hole and filled bays untill they hit the right pressure. Regular loose blown insulation will settle over time and leave the top few inches empty, so if you go that route, tell them you want it dense-packed, not just fluffed in.

I find it hard to beleive that just blowing material until the crew hits a certain pressure will completley solve the issue, especally given the size of the cavity. Even if they are using a dense-pack method, you are only filling the joist spaces, and that leaves massive amounts of uninsulated space above the drywall and between the beams that the blower can't reach. If you're trying to keep the cold air out, simply stuffing the joists isn't the whole plan. You're going to need to account for those open top sections as well.

You definatly need to think about air sealing before you blow anything in there. If you don're just filling the joists, you'll still have massive heat loss around the perimeter of the cavity. I did a similar job once where we found the main source of leaks wasn't the hole, but the gaps around the 2x8 top plates wich were open by nearly half an inch all the way around. Make sure that perimeter is taped and sealed first to get the biggest improvement.

Then you can proceed with filling the joists from below.

Update: went ahead and had a crew dense-pack it through the light hole, and both rooms alredy feel way better. That said, there's still a draft along the outside wall that didn't go away. The air sealing point in the replies got me thinking I shold have done that first. Is it still possable to seal the top plates now that the cavities are full, or would I have to pull the insulation back out of the way?