NOTE: First of all, I am NOT a tax person, but a fellow user, so keep that in mind. I'm not offering advice, but I'll tell you how I handle unexpected income, such as a conversion, in my situation.
Without regard to the conversion, by the end of this tax year--either through withholdings or estimated payments--will you have paid at least the same amount of Federal tax as your total tax liability on your 2019 return?
I personally do not pay the tax upfront on any conversions as long as by the end of the year I know I will have ended up paying through withholding and/or estimated payments at least the same amount as 100% of the total tax liability I owed and paid the prior year. That's called a Safe Harbor exception to avoid an underpayment penalty. Another safe harbor is if at the end of the year you will have paid at least 90% of your final current year 2020 total tax liability. There's a bit more detail to Safe Harbor rules, such as having to have paid at least 110% of prior-year total tax liability if your AGI is over $150,000 (over $75,000 if married filing separately), or at least the 90% of total tax liability on the 2020 return. There are also special rules for farmers and fishermen.
Again, as I mentioned, I'm not a tax person, so I'll have to leave it to any others to discuss more details of the Safe Harbor rules.
But here is an IRS publication that may be helpful to you, which explains the rules in more detail:
Pub. 505 - Tax Withholding and Estimated Tax
https://www.irs.gov/pub/irs-pdf/p505.pdf
NOTE: These are Federal rules. it's possible your state has estimated taxes rules that differ from the Federal Safe Harbor rules.
