Carve braces in a dish?

I expect you will wonder what happened once I finally get this ukulele built! Until then I seem to be a veritable question Mill. The rabbit hutch of questions... Here's what I'm working on. An acquaintances said come on over and he would hook me up with his 15-foot radius dish to set the braces on the back of my tenor ukulele project -first instrument. When I got there I learned that it was actually a 12 foot radius dish which was fine. And so in the interest of time, after leaving it clamped up there for an hour and a half, we used spring clamps to secure the braces in place and I took it home. But now I am thinking how do I carve these braces down without the curved radius dish? I don't feel comfortable doing it on the flat. I do have a 20-foot radius dish, but... ?
My man is about 45 minutes away on a good day so if I want to do this soon going back to see him is not an option. What would you do in this case?
Bless you all!

I have a metal rather than woodworking background but some of the principles applied are common and can produce a more that good enough functional result though maybe not perfection.

To put a radius edge on sheet metal I'd put a centre punch mark in it and use a pair of dividers to scribe an arc. I'd then cut and file metal away to just meet that arc. If the arc was so large a radius as for its centre to go off of my material then I'd clamp a scrap piece or two to it. For a (approximately) 12 foot radius I'd be clamping to the work bench or two work benches and then marking an arc with a (anchored) taught cord and scriber. I'd then form the radius on the workpiece by cutting and filing metal away to match the marked arc.

That method could be translated into woodwork easily enough. Use a chisel edge hard lead pencil to mark out with and planes and course sandpaper to cut away the excess wood. The result won't be perfect - a bit depends on your eyesight and skill - but it might well be near enough for your purposes. Worth a try?

Once the glue is set it does not matter if you care the braces in or out of a dish.

If you plan on making more ukuleles then you might want to purchase or make a dish for your backs. When carving I find it nice to have support under the entire length of the brace. Also the back can be cracked by holding it down when carving if you're not careful.

You stick something under the back, that takes up some of the gap. It only needs to be a little bit wider than the brace itself. A bit of thin wood, plastic, anything. Put it under the end of each and every brace, just don't go at the braces like a demented Ukulele builder. Simple, no need to complicate matters. It will be fine.

I've always carved on a yoga type matt, or flat table. If i was richer id get a dish just for carving

Get a fairly shallow box a bit larger than the back, fill it with fine wood shavings and press down to make a 'nest' to fit, and cover with some thin cloth to protect against any scratches. This will give the back enough support to carve the braces.