On this retrofit project, the home has vaulted ceilings, so plenty of room to add insulation at the interior ceiling and re-finish. There's existing 7.5" (poorly) insulated ceiling joist bays with 1/2" drywall finish, so one option is to simply add say 4" of EPS to the assembly, screw & glue to the drywall, and then finish that with perhaps cedar panels.
Question is, is this a durable assembly, one that won't have moisture or other problems? Ideally we'd add it on top of the roof sheathing, but the roof is pretty new so theres no interest in re-roofing. In the Pacific northwest a mostly heating climate we dry from the inside out, is this assembly going to put the dew point in the wrong place or something? Anyone ever done insulation added from the inside retrofits?
If the insulation is on the inside in a heating climate it needs to be an effective boundary against vapor transmission to keep moisture away from a potential condensing surface. Especially if there is a tongue and groove ceiling finish. A good method would be to install two layers of foam board with the seams offset in both directions and taped. Penetrations for electrical boxes should be treated carefully.
On the other hand, one wonders whether it wouldn't be easier, more cost and labor effective, and do a better job to take down the existing ceiling and insulation, foam the cavity,and put a ceiling back up. For a better job, add your foam board with taped seams, and install new sheetrock or whatever on furring. This has the added advantage of bringing the existing marginal cavity insulation up to snuff.
I would lean more towards Ed's last solution with a caveat, I am assuming this roof is vented - if so I would trim down some XPS panels as firring strips 1.5" x 1.5" placed against the roof sheathing against the joist (2 in each bay - maybe 3 if 24" OC), install XPS panels foaming the seams, between panels & the edges inside the cavity with 2 layers of 1.5" panels & a final 2" panel. You know have 5.5" of foam, still have ventilation and can now easily install either drywall or cedar. Trying to install drywall or cedar with 6.5" connectors (that is what your system requires) can be a nightmare (especially on a finished ceiling)
Now if there is no venting - rip, remove & Closed Cell Foam
Either which way you are looking at a better structure with a better finish --- I would also recomend checking everything with an IR camera / blower door to verify everything is done properly / sealed tight
The Dow Thermax sheeting is fire rated and depending on local codes sheet rock may not be needed. I did install 1/2" plywood screwed to the trusses through the foam and sheet rock. The plywood really being the only way to fasten the cedar to the ceiling. Using paneling the plywood's not necessary.
Be sure to do the building science for your climate.
Leo K. PE