using your math:
<<max penalty if not paid estimates is 60000 *0.22 * 1% * 9 = 1188? >> it wou.ld be times 7 (Sept --> April). and the current annual interest rate the IRS is charging is 7%.
<<how does the penalty change if I pay 60000 *.22 to IRS in August? >>
should eliminate it.
or if I do whole conversion after Sep 15 and pay full taxes owed then in Sep - same thing - if you do the coversion AFTER Aug 31 (not Sep 15), then the estimated payment is not due until Jan 15 in any event, so using your math: 3 months times 7%/12 *60,000*..22 or $231
chances are any underpayment will be even less than your worst case due to what is called 'safe harbor' which is based on how much tax you paid in the prior year (2022). but let's not go there - you have your 'worst case'.
