Since these taxes are not a business expense, it would surprise me if the IRS viewed the fees charged to pay these taxes as a business expense.
One point where the nuances are often overlooked: passthrough entities are not taxed for federal income tax. It's an obvious concept, with some interesting consequences.
For example, the business (or schedule C in this case) does not pay tax on the income. The individual pays tax on their share of income. If you were paying quarterly estimates on W-2 income (instead of withholding), would you expect the fees to be deductible in that case? I wouldn't, so by extension I would not expect the fees you mentioned to be deductible.
Note: I have no case law to support this, just one guy's musings.