Can I make a payment now on the directpay.irs.gov website, applying it to my 2018 form 1040, and then file through TurboTax through a later date with an extension?

Yes, you can make that payment to the IRS. Just be certain that your name and SSN are an exact match to your Form 1040 tax return, and that you indicate the payment is for 2018 Form 1040.

In  TurboTax, as you complete the request for extension, there is a place to enter the amount being paid with the extension. Enter the amount of your directpay payment there, so it is accounted for later, when you complete and file the tax return.