And of course, minutes after posting I find a solution.
&page%5Bcount%5D=1000
That does the trick. Weird that I have to specify it since documentation says it returns 1000, so I would assume 1000 would be the default, but whatever. It works now.
If there are many pledge events, then the returned result count may be adjusted down. However if you are making requests without pledge events and getting 20 results despite requesting page numbers and pagination correctly, likely something is wrong with the call. Check out how the WP plugin does it:
When the count query param is not provided, the documentation specifies that 1000 results will be returned. If that is not the case the documentation should be updated.