Hi David,
Kevin and I checked with the team and learned the 1k/day/domain limit is a soft one intended to prevent potential abuse. Since I assume you have a legitimate use case, you should be able to open a support case requesting a limit increase.
Make sure to include a description of the legitimate use case, the domain in question, and what you would need the outbound Web Request limit daily raised to.
We'll work on clarifying this process so others know that 1k is a default limit, not a hard cap, and how to request a raise. We may also increase the default limit in the future to reduce how often customers will need to open these support requests.
Update 6 June 2022:
We will be raising the default limit for outbound Web Requests to 5,000 per domain per day in the near future. Customers who have a legitimate need for more than 5k calls should submit a support ticket with a description of the use case, the domain in question, and how high they would like the limit raised.