Busyflyin, we're not talking the same thing. First of all, a SIP panel does not give you anywhere near the R38-R40 of insulation you need in your roof system. So if you install a SIP panel over vertical battens, you've created a nailing surface, but you have neither a vapour barrier, nor enough insulation, and the inside surface of your roof deck (the part you see from the inside) will be at or below freezing in winter and any moisture you have in the inside air will condense there. Not a good scenario.
Let's look at this step by step. Your current situation is as illustrated in Image1.jpg.
E is your current deck, G are the 2x6 rafters and F is the space between them.
I am proposing that you fill in the space between the rafters with blue styrofoam, install a vapour barrier under this (across the rafters), and then install wood planks or boards across the rafters to give your the "wood" look to your ceiling. This is shown in the following image.
Note that the inside space between the rafters (F) is now filled completely. Then you install the vapour barrier below this (H), and nail your wood planks to the underside (I). So far, you've got the vapour barrier that prevents moisture from the cottage interior air from reaching the cold parts of the roof. However, note that the building code in some jurisdictions requires that if the space between rafters is filled with foam insulation, that a fire-proof material (like gyproc) is used as the covering layer. So you need to check the local codes.
Next, on the outside, you add the two inches of blue styrofoam insulation, place 2x2 inch purlins (oriented vertically) over these, place the OSB on top of the purlins. This is shown in the following image.
The two inches of external insulation (D) is laid on top of the stripped deck, then the 2x2 purlins (C) are laid on top, and then the plywood or OSB (A) is laid on top of these. You need to hold the whole assembly together with either very long nails or screws (J) that penetrate into the original rafters.
This assembly then gives you the vapour barrier (H) on the warm side of the insulation (F & D), a ventilated air channel (B), and a deck surface (A) on which you will need to install the underlayment and shingles. The combined R-value of the insulation should be about 36-38, which should be sufficient for your location and usage. The two inches of air space is the minimum required, but you therefore meet the minimum. In winter, the freezing point of the roof assembly will be located inside the insulation, and therefore you should not have problems with condensation (AS LONG AS YOU HAVE THE VAPOUR BARRIER ON THE WARM SIDE OF THE INSULATION, AND THE BARRIER IS INTACT).
In effect, you will be constructing a sealed, ventilated cathedral ceiling.
Anything less than this will give you problems, in my opinion.