How deep can I bury it? 3-6''. If you plant it at 45 degree you can get more shoots from the base.
Does it bloom on old wood? mostly yes, but after flowering prune the stems by 1/3 or a half and fertilize. You will get a second flush later.
How can I encourage it to bloom taller? Your clematis will mature to a height of 6-8 feet. If your support is tall enough your clematis will just grow to the promised height and start to produce flower higher. If your support is short you can bend growing shoots over your structure. In this case, the next year you will have old wood on top of your support. If your hydrangea is close enough you can let some stems from clematis twine into hydrangea and beautify it before it will produce its own show.
Can you use different variety? If you decide to go with different variety there are lots of new cultivars that:
1.flower from May to September ( they start on old wood and then go on on new),
2. can be pruned hard (no mess hanging in winter) and
3.are shorter in height. In this case you can plant your clematis under the bush ( as I understand munchkin oakleaf hydrangea is not very tall) and the bush will be its support. Good luck.