Getting R38 in roof with 2x8 rafters
For Future Viewers:

No-one's forcing you get to R-anything, yet &amp; it's coming people, but it's great that you want to. I'd call the Roofer back &amp; get the leak fixed first. Whether you can get to the leak &amp; don't fix it or cover it &amp; never see the leak doesn't stop the leak or building rot.

However, you must (&amp; I mean must) have joists below those rafters &amp; they can even be built-up. Your idea is right, it's just not in the right location. Unless, your overall plans are to finish the attic.

If that's the case, then you don't need anything more than R-19 for that new segregated room's roof if you already have an R-38 done on the floor for the rest of the home's cap. Sure, more is better but not at the cost of Roof, Gable &amp;/or Ridge Vents.

The roof's R-19 for a finished attic there would be best as just Polyiso boards with as much air space as you can give the roof to breathe. Literally board from the eave's venting all the way up to the Gables or Ridge to actually make a dedicated &amp; drastically reduced venting highway for improved everything.