Sorry to say you are trying for the best of all worlds, but you probably will not get all of them. I'm just about to start a house with 19' ceilings with exposed glu-lam beams. I had one tough go-around with the architect over roof design. He wanted to use 2x12s or 2x14s. Having built homes I can tell you it is bad news for asphalt shingles to put the directly over dead air space. You can take a 40-year shingle and get it to curl and crack in about 15 years doing that. I demanded, and got, 2' deep open-web trusses for my ceilings so that I can install the 18" of insulation I like to use. Your suggestion of using insulated panels sounds good on its face. However, let me tell you that in pricing one home using insulated panels it came to roughly the same price as if I'd used 2x12s for the wall framing. They ended up being quite expensive, and if you want to use them on a roof expect to pay a good amount for the crane rental. Of course, you could just get small panels and get some help setting them on a roof, but with those panels keep in mind that every seam you have means either and I-joist or the manufacturers joining system, which costs additional money.
Even if you do put on these panels, you still will be nailing shingles on over dead air space. Shingle manufacturers suggest ways to lift the shingles off of the sheathing so that air can circulate behind the shingles and significantly extend their life expectancy. The bottom line is that each additional step costs additional money. On one house I did I left some of the beam exposed, since they were quite deep, and on their sides nailed on 1x4s on each side. I then installed 4" foam board between the beams and behind that applied some tongue&groove knotty pine, which I varnished. That left some exposed beam, gave me about R-28 insulation, and left a very nice rustic cabin appearance on the ceiling. If you want something more modern looking I'd just use 5/8" drywall instead of the knotty pine. With this type of set-up you still should have a minimum of 2" of unobstructed air space between the back of the foam and the roof sheathing. With vents under your eaves and some type of ridge vent you can use just about any type of shingle and meet the manufacturers warranty requirements.
All of this being said, none of this will come very cheaply. The price you mention figures about $2.30/square foot, which is not all that much. The second method I suggested is primarily interior work, so it does not really upset any of your roofing, but just the foam board should run something over $1/square foot, and that is before renting scaffolding, buying drywall, which has skyrocketed in price, and doing finishing work. My recommendation would be to not use the insulated panels. Your budget will be blown long before you even get them up on the roof. Hope this helps.