Since you already have to withdraw income from the inherited 401k, the question to ask is if the larger withdrawal will push you into a higher tax bracket. If so, then the extra added cost is the increase in tax rates on the added income. Keep in mind that adding $200k+ to your AGI will also push you into the Net Investment Income Tax if you are not already there (it kicks in at $200k single / $250k MFJ).

You would then compare that extra tax paid above your current marginal tax rate to the cost of the interest + closing costs related totaling out a mortgage. So for example if you are in the 22% bracket 10k below the top and the extra withdrawal pushed you into the 24% bracket, the extra tax cost would be 2% of 190k.

However, since you want the total tax cost to come from the withdrawal as well, you run into a bit of a problem, because taxes aren't flat, as noted above, so you can't use a recursive formula to figure it out.

My recommendation for getting these answers is just to run a pro-forma tax return using this year's tax software. Unless there is a major overhaul in tax law the results will be very similar to next years taxes, probably slightly high because there haven't been adjustments to the inflation-indexed numbers.

And don't forget state taxes if you have them.