Improvised inflated Monolithic Dome ???

I am not intimately familiar with the inflatable structure sometimes used to make these, but lets say you got two rolls of moderately heavy gauge plastic sheet, cut off two identical rectangular pieces, one on top of the other, and used good tape, like "Pipe Wrap" to seal all the way around, except for one spot where you have a piece of 3" PVC pipe and a valve, and in it in turn, some nipple or valve that can be hooked up to a very small compressor. First, something is used to basically inflate this new big bag, and when full, the vale is turned off to keep the air in, and the small compressor is used to somehow keep it filled to tension.
Maybe somehow affix something like burlap that is synthetic, to hold the mix sprayed onto it in place.
Then you spray the mix onto it just like the 'pros', and make some odd semi-rectangular shell.

Does this sound like it would work?

Check out:

http://www.flyingconcrete.com/otherformsys.htm

and

http://www.flyingconcrete.com/lloyd-turner.htm

the whole site is great, but those may be where you want to start.

Looks great, except it doesn't say much about how one is supposed to use the foam.
How is the foam supposed to be applied? Getting some proper machine would be very expensive, and using small cans of foam insulation would be very sloppy and also very expensive.

- Have any insights or sources regarding this facet of the construction ?

I don't know if local contractors would be willing to work inside a bubble, but I don't think it's very expensive to hire somebody to spray foam for a 'normal' house.  I'm pretty sure the foam on the above pages gets strong enough that they spray shotcrete both inside and out, but it may have been another site that mentioned that. 
There are some people doing similar things with papercrete, but I don't have a link for them.  You can build your own sprayer for papercrete.  There are several plans on the web.  If papercrete interests you, there is a papercreters group on groups.yahoo.com .
Anyhow, even the way they put together the tyvec bubbles should give you a starting place.

Hiring people and equipment, especially for something specialized like this gets expensive real quick, and often means those hired people and equipment having to travel to your location, which adds even more to it.  Its not for me and what I want to do.

I have seen how they build a house out of pink foam board and then shotcrete it inside and out, and the shotcrete does stick. If I were to focus primarily on shotcrete, that would likely be the way I would go, but for me that would be wasting all the gravel I can get out of the ground and use for cast concrete.
Otherwise, I love shotcrete and what can be done with it.

I can understand why they want the work done from the inside, otherwise I would just hang some kind of cheap burlap, fabric, fishnet or similar on the outside to hold the shotcrete.

From a building science perspective, better to get the insulation on the exterior. Closed cell spray foam by a contractor would be the best choice and shouldnt be that expensive depending on the size of the structure. There are also DIY spray foam kits.

@SpringtimeHomes: If you have any links or sources for such kits, please do let us know...

Fine Homebuilding #221 just had an article on them.

Foam it Greens 602 kit
Dow Froth pak 620
Handi Foam Quick Cure
Touch Nseal 600
Tiger Foam quick cure (cheapest for author at 565$)
Veri-Foam system 50

Be very careful about following the recomendations. Improper app will bring the dreaded fishy smell.

http://www.greenbuildingadvisor.com/community/forum/green-building-techniques/22156/diy-two-component-spray-foam-kits-can-produce-smelly

http://www.greenbuildingadvisor.com/blogs/dept/musings/spray-foam-jobs-lingering-odor-problems

Check out the thin shell sections of Mortarsprayer.com Lloyd Turner's design and way to make a form/balloon is shown also. The quote I got to foam the inside is only about 10% higher than the cost of DIY foam off the web, If you are doing a big building, say 40 feet diameter or more, check out basalt rebar. It is much easier to work with, stronger and lighter. Made out of rock, not iron ore. Costs more than steel, but saves on labor and concrete. The Mortarsprayer Tirolessa sprayer will save a huge amount of labor.

You might want to look at surplus parachutes. You can find really large ones on ebay and at some surplus stores. If you use a fan and have the perimeter secured to a base wall, seems like you could shotcrete/spray-insulate the exterior/interior as you please.