Years ago I interviewed to be head seamstress at a very upscale dress shop. The rest of the sewers were eastern European women who mostly couldn't speak English, so they needed an American basically. The pay was excellent & the sewers had the opportunity to charge whatever they wanted to a customer if it was a rush job they did on their own time.
What a gig it would've been. If only I could hand sew! I knew nothing about garment construction, esp. hand finishing. I could corner a drape & close a pillow by hand & that was it for me.

My old drapery boss used to say that the way to know your price is right is;
--- If they scream bloody murder when you give your price it's a little high
--- If they jump at your price w/o arguing, it's too low
--- If they try to negotiate it down a bit, it's just about right.
Also, custom sewn goods are prestige goods to the buyers, they want to brag about how expensive it was, check the prices the shop is charging for an idea of how high you can go.
How long do the pieces take to sew?
What's your over head?
What wage do you need per hour? Need to translate that to your time/piece. Remember you need to figure a PROFIT in also!

It sounds to me that you have what they need, so don't under-price your skills. You can always come down, but going up is another story. So many seamstresses price themselves way too low & give away their skills & knowledge...

It's odd they want to pay piece work on this since it is not a factory/production line setting. Difficult too cause if you are good and faster, you are worth more... BUT even if you are good but slow no one wants to pay a real high price for a slow worker who can't hardly produce. I subcontract work (alterations) in tailor shop and I work as an independent sub-contracter. I get 60% of the charges.