What is the best way to insulate an unvented interior vaulted ceiling with 2x6 rafters?
You cannot completely fill the attic space like you can a wall cavity. Remember, you'll need at least 1&quot; air space above the insulation for &quot;attic ventilation.&quot;
If you choose to use the 2x6 roof joists, you'll only be able to &quot;fill&quot; the joist space up about 4.5&quot;.  So, your choices are 3 1/2&quot; thick batt insulation for an R-value of about R-11.9 or rigid insulation board for a R-20 to R-30, depending on the type of board.
If you choose sistering 2x10's, then they have a net depth of 9 1/4&quot;. Therefore, leaving about 1&quot; for venting, the net depth of insulation should be about 8&quot; or so. That would give you R-19 to R-21 with batts or R-30 to R-60, depending on the type of board. (By the way, the R-60 is with polyisocyanurate boards, which are very expensive.)
Also, you're correct in assuming there is a significant R-value reduction because of the 3&quot; of solid wood joist space.
If you furr down a 2x4 &quot;ceiling&quot; joist system, you could create a deeper attic space and use blown-in insulation, which is much cheaper. However, you'll need to verify that the 2x6 roof joists can support such a load. (Note: If you have an average load of about 25 lbs. per sq. Ft. Live load and 15 lbs. per sq. ft. dead load, then my calculations indicate 2x6 joists at 24&quot; oc will only span about 8' to 10', depending on the grade of lumber. If the span is further, you could add 2x8 or 2x10 ceiling joists and support the existing 2x6 roof joists &quot;up&quot;.
Also, you indicate the slope is about 27 degrees, which is slightly steeper than 6:12 (26.5 degrees). Blown-in insulation will tend to settle down to the walls, become ineffective and block the vent space on that steep of slope. Consider lowering the new 2x10 ceiling joists down to 2:12 pitch (about 9 degrees).