How to optimze a coil for needed voltage?
I'm sure there's a professional tool, but I would just use a spreadsheet.

Choose your constants - wire diameter, hole diameter, length, etc, and let it work out Area and Nturns (assuming some wire filling fraction, maybe 50%), then V. , Also length of wire, and then resistance, and cost.
Then play with the constants, try a few scenarios, even plot some graphs.