Oh what a shame you already did the roof. That would have been a perfect opportunity to add rigid foam insulation boards above the roof sheathing.
A vented roof is definitely better from the perspective of shingle life and moisture resistance, but with such shallow rafters and an unwillingness to lose any ceiling height, that's not an option. If you go with a vented roof, you will need to use 3-4" or so of rafter depth for the ventilation channels (depending on roof pitch; lower pitch requires deeper channels), giving you not much room to work with for insulation between the rafters. If you are unwilling to reduce the ceiling height by installing foam or mineral wool boards across them, then the room will be very uncomfortable as a result.
Your best bet at this point is to get someone to apply a full 6 inches of closed-cell spray foam to the underside of the roof deck between the rafters. This stuff is R-7, so you'd wind up with nominal R-42 between the rafters, which isn't bad. Taking into account the thermal bridging of the rafters, the actual performance would be more like R-37--not terrible, but not great. If you go the spray foam route, hire it out. The DIY kits wind up being about as expensive as hiring out the job in most locales. If you thought the upcharge to add foam to the roofing job was high, wait till you see what the spray costs. Expect $9-14 per square foot of attic space.
You can try doing this yourself with cut-to-size foam and Great Stuff filling the entire faster bays; this is referred to as "cut-and-cobble." You will definitely save money, but it is a messy, time-consuming, un-fun, thankless job, and it is more difficult to get a perfect air seal (which is absolutely required) with this approach than with spray foam. Furthermore, the R-value you'll achieve will be lower because there is no R-7 rigid foam commonly available. XPS is R-5 (yielding a whole-roof R-value of R-26) and polyiso is R-6.5 when it's hot but R-4.5 when it's cold (yielding a whole-roof R-value of between R24 and R-34 depending on the temperature).
I strongly recommend accepting a 3" loss in ceiling height and putting polyiso under the rafters. If you can live with that, you can detail the polyiso as your air barrier by taping all the seams with housewrap tape. Then then fill the whole rafter bays with cheap cellulose, which is hydroscopic so it will help wick water away from the roof deck if it does get wet. This should yield you a whole-roof R-value of R-39. Then cover that in drywall. You can do it all yourself and it won't break the bank. To improve the R-value, just add more inches of polyiso under the rafters; each extra inch will add another R-6.5. The cost difference between this and 6" of spray foam should be dramatic--maybe 5x cheaper or more.