The biggest restriction is that you can only replace the IRA funds once every 12 months. So you can’t do a quarterly conversion, have Vanguard withhold some money, then replace that money within 60 days. Well, you can do it once. Then you have to wait a year to do it again. The other three quarters would be out of luck.
Making estimated tax payments really isn’t that hard. Mail a check with a 1040-ES voucher (all that needs is name, address, SSN, and amount you are paying). Or sign up for EFTPS on the IRS web site and schedule your payments in advance - or make them on the spot. It’s really no harder than paying any other bill you might have.
–Peter