After 4/15 you will likely only be able to schedule a "right now" payment.  The only disaster where the IRS changed the programming on this is when returns were due 7/15 during COVID.  There are dozens of disaster declarations every year (sometimes impacting entire states) but the IRS systems cannot automatically apply these extensions to scheduled payments.  They have gotten better at abating penalties when your zip code is in a disaster area but have done nothing to make the payment process more flexible.

I stay out of the tax payment processing business and stick to the tax return filing business.  Clients are free to make their tax payments however they deem appropriate (I generally encourage IRS Direct Pay but some folks still want to write checks, send certified mail, wheelbarrow full of pennies, etc.)

Rick