Lets assume this is a good idea, and that this is the plan you want to go forward with.
when should I actually make the withdrawal? Is there an amount of time
before applying for credit I should do this, or a smart strategy for
timing or pacing it?
Because it should only take a few days to go from Roth IRA to your bank account, there is no need to do this until shortly before the settlement date. You don't want to wait until the last day because you need time for the funds to get top the back, and then get the cashiers check from the bank.
During the loan approval process you will be asked to identify the funds for the down payment. The lender should not require moving the funds until lets say a week before the actual settlement date. They will be able to give you a date.
The reason for not doing it in advance is that there can be delays in the closing process, or the deal could fall through. You don't want to remove the funds from the IRA, have a delay, then have it collapse, and then be unable to redeposit the funds into the Roth IRA.
It is also possible that you might not need to move as much money as you plan to, because the house might not be as expensive as you think or the interest rates are different then you expected.
It feels a little odd to leave it in the market until say, the day
before I need it, but on the other hand if I pulled it out, say,
today, I'd potentially miss out on six months of gains.
If you are concerned that a drop like 2020, or some of the other recent events, will not leave you with enough money for the down payment; then you could move the Roth IRA funds into a more conservative investment and still keep them as a Roth IRA until it is time to cash in the funds.