"I would like to count my withholdings as paid quarterly"
No, you don't want to that and you are not allowed to do that. Withholding (unlike quarterly payments) is treated as withheld evenly during the year, no matter when paid. That alone, prevents an underpayment penalty for bad timing.
Common example: Retired person has his entire pension or IRA withdrawal in December and has enough withholding taken out to cover the pension and a big stock sale made back in January. There is no penalty, even though the tax on the January income (gain on stock) was not paid until December.
