Replacing ceiling joists with rafter ties higher up on the rafters

I commented above that the question can't really be answered, but I have a few thoughts to share...

Would it be possible to raise the ties up so that he could use a single 20' board for the full span?
My concerns are that the ties will sag due to the long span, and that the rafter tails may not be adequately anchored to the wall plates if you remove the existing ties. The ~2' rafter tail shouldn't be a concern with respect to flex or strain. That's pretty short for a 2x6.

Would it be possible to skip every other rafter?
Yes, but then you put even more stress on the connections between the ties and the rafters, and between the rafters and the wall plate, for each remaining tie. Connection strength is key.

Would doubling the ties on either side of the rafter help alleviate lateral force?
Lateral force isn't really a concern with respect to tension on the ties themselves. It's a matter of the connections, as I said. Adding more lumber doesn't necessarily help with that.

We made a similar change once. The contractor put up cross-connected ties -- sorry, I forget the proper name -- which run from one wall to near the peak on the other side of the ridgeline. You lose about a foot of ceiling height at the peak (inside) but then you have a cathedral ceiling without any cross-ties at all. Aesthetically much nicer.