Yeah thats a tricky best practice that we havent attempted yet. The goal is a vented air space so you have eave and ridge venting to get right as well. The projects Ive researched that seem to favor it put the purlins diagonally. I would consider going through the trouble and expense on a retrofit but with new construction higher performance can be done more cost effectively from below the roof deck.

Youre right on with choosing screw down metal over shingles right now IMO. By going with a highly reflective color you can probably achieve the same performance

Shingles aren't that expensive now. I think I am about $5k for shingles and $12k for metal if memory serves.

Price for shingles is about 80-90 bucks a square here. Unpainted galvalume runs 1.80 a linear ft for a 3 ft wide panel. So about 60 bucks a square. I know the metal flashings and trim add to that cost but total cost of materials would be close to the same.

Any thoughts on the use of the purlins?

Purlins were used when sheathings weren't around back in the day. It was common for metal roofs as well as wood shingles to use purlins. There's no problems running metal over sheathings these days but the important issue is making sure you have a decent underlayment(s) that works for your area of your build. Standing seam is typically more pricy than middle of the road shingles. Shingles can get pricy using the laminated, heavier shingles but around here, metal is more but when installed properly, has more longevity. Depending where you are building, it's often wise to go with a heavier gauge metal, worth the cost.

The only concern with not using purlins would be in a situation where you have high moisture build up under the panels. The purlins would be staggered with openings to act as a drainage plane and again, a quality underlayment. It's as usual, geographic specific.

I live in Northwest Florida. They used synthetic felt on the roof deck. I believe the metal I was quoted was 26 gauge.

I lived a short while in Gulf Breeze just outside of Pensacola. High humidity and pretty chilly, even icy in the winter months. You might inquire how other metal roofs are being installed in your area by reputable roofers/contractors as the purlins would allow the underside to breathe. We went with 29 gauge on an outbuilding on our build in the Sierras. Layed it over the underlayments/sheathing but nowhere near the humidity levels that you have in N.W. Fl.

Humidity is quite the issue! I have talked to a couple of roofers in the area and they use the purlins. My roofer is also my father in law so it is a delicate situation telling him that he may be doing it wrong!

The best system is structural panel sheathing, Grace Ice & Water Shield and metal roofing. I don't know what purpose the addition of strapping over the structural sheathing would serve. Roof venting would only be necessary in an insulated cavity below the roof sheathing.