If you don't want to use framing members, especially if you're going with a masonry roof, you're gonna make it harder on yourself. But brick vaults are awesome.
Question how you are going to insulate your roof since you are opposed to having petrochemical in your house? Your system is going to interact as a whole. I buy discounted bunks of various rigid foam either used or grade 2. I guess it depends on your motives:
footprint, indoor air quality, natural philosophy, cost... Im not interested in debating this, I'm just saying that these values need to be addressed with each builder and owner so that one can appropriately choose/build a durable, highly performing structural system.
I also prefer ferrocement roofs because I'm low on time, but have done bag dome, Adobe squinch, brick vault. Metal roofing, epdm and roof tiles all for the pizza toppings.
If you aren't much of a mason, how about Quonset sections? Or frame? Or ferrocement? Easier with permits, quicker, cheaper.
But if you mason your roof without a slab, keep it simple, keep your spans small. in Ohio, remember that you need good insulation and good roofing or decking on the top. In your climate foam on a masonry roof is a good insulation combination. Or for foam free: cellulose in framed roof for the win.
As far as mortars: pure gypsum and lime mortars, maybe a curtain wall or veneer; Structural cavity wall -- I'd pass; Brick vault--i'd go inside that building but I would not build or live in it.
Ferrocement is way quicker, cheaper, diy-able, and reinforced. It can easily be thickened to match compression if needed for second stories. If you need brick and you're asking advice on permies, hire out
local mason that you can labor under, or grab a crew from the Mexico, the East, or Africa. it's not that DIY. (Doubtful that an engineer would stamp brick vaults for a DIYer.) If you do DIY, think simple catalan barrel vaults, one reusable formwork that repeats itself. Yes groin vaults are beautiful, but every diagonal groin rib adds up, every dome adds up, every compound cut brick adds up, as does every piece of complexity or sculpture, every nicho or wide span vault. With the busy pattern of brick, i think simple forms shine. (Groins can be framed and drywalled or ferrocement). If you keep it simple, you have a much higher chance of getting a roof overhead, and will have a place to display your Gaustavino / Gaudi
coffee table
books. Price your time and examine how deep your pockets are right now. Brick also looks good on walls or floors instead...I also like to avoid valleys no matter the roof construction...
Edit: forgot his name, but there may still be a mason for hire in yellow springs that could do you brick vaults.
Edit again:
http://www.structure1.com you may want to contact their engineers, or a similar firm licenced in your state about hire.