Vaulting ceiling and removing ceiling joists without risking the integrity of my roof system?
Yes, you can remove the ceiling joists and “vault” the room, but you have several issues: 1) unusual structural system, 2) loss of attic insulation, 3) heating

1) The existing roof joists are  supported by a complex set of ridge beam, intermittent vertical supports and a “strongback”. In order to remove the ceiling joists and vault the space, you’ll need to install temporary supports under all existing roof joists, remove the existing vertical supports under the ridge beam and then slip a NEW ridge beam in under the existing ridge beam. (This is going to be somewhat difficult because the existing ridge beam is slightly lower than the roof joists. The new ridge beam will need a notch so it can fit tight to the roof joists.)

After the new ridge beam is in place and supported with a NEW post at each end and each joist clipped to the beam, then the existing ceiling joists and temporary supports can be removed. 

The new posts will need adequate footings. You may be luck, because the existing strongback probably has some footing under it at each end. 

Installing the beam will be difficult because it could weigh 17 lbs. per foot (for a 6x12) up to 25 lbs. per foot (for a 5 1/8” x 18” glu-lam). Wiggling that into place will take some skill. 

2) New attic batt insulation can be installed between each joists, but keep 1” air space between the insulation and roof sheathing for venting. (Be sure to add soffit vents and ridge vents in EACH joist space.)

3) consider how you’ll heat the space...ducts?