First, lets make sure that what we are talking about is you coming up with the money from someplace else, to cover the amount of the loan.
I believe the SECURE act extended the deadline to make a rollover to cover the offset to April 15 on the next year, not just 60 days, assuming it is a "qualified offset." If you deposit the corresponding amount of money into an IRA, that is your "rollover" that puts the money back into tax-deferred retirement savings, and you don't pay income tax or the 10% penalty for early withdrawal. This is not "mixing pre-tax and after tax dollars" in the IRA, as long as you complete the rollover by the deadline and you tell the IRA in advance, that this is a rollover and not a regular deposit.
Any Roth conversions you do are entirely separate. Roth conversions are subject to regular income tax but no penalties. If you rollover the offset funds into an IRA, and then later do a conversion from the IRA to a Roth IRA, that is a taxable conversion just like any other and the original source of the money doesn't matter. They are two separate events.
You have an "offset distribution" from your 401k, you will get a 1099-R from the plan administrator that must be reported on your tax return. After entering the 1099, Turbotax will ask what you did with the money, and one of the choices will be that you rolled it over into another qualifying account.
