1. Open Ally Bank account (there are others but this definitely works)
2. Setup recurring bill pay for your check payment.
3. Setup recurring external transfer from your hipster bank to Ally or equivalent in step 1.
$6.99 isn’t worth replacing the above system that has another distinct advantage over this: you have two layers of cushion from your main account.
My understanding is that this service will print your account details on the check. The “bill pay” services typically are not writing checks against your account, they withdraw the money and use their own account.
Knowing the horror stories of intercepted checks that are cashed, this is not a triviality.