I've typically done these how Matt suggested with good results but in two variations.
1. Get pre-veneered MDF both sides, rim miter and raise. This is particularly challenging to not burn the veneer when you sand flush unless the veneer is thick, I would not recommend you try this on your first job or at least practice with smaller panels until you dial in your process.
2. Rim miter to raw MDF, then lay-up the panels, then raise them. This is far easier and provides a much cleaner look. You also hide gluelines and squeezeout if you're going to stain them, there are far more advantages. If you don't have the capability to lay them up take them to someone who does or invest in a press if it's a large job.
You mentioned local shops not wanting to add a backing veneer, they clearly don't have the experience and I would steer clear. If you ever layup sheets without properly balancing the substrate they will warp, almost always. The only time I get away with this is when I do things like bench tops but otherwise always a backer veneer. As others stated you can get just about anything, the cheapest veneer you can find and it will provide the counteracting forces needed to stabilize a laminated substrate.
And remember, keep it simple. As others stated go to nominal numbers, 30" is a huge waste. Tab up some quick numbers and present it to the client, and watch as they go for the economical option most of the time.