You might be able to hack something together that has the same effect using a code page. If you pass whatever parameters you're using in the API call to the code page instead, you can read those parameters when the page loads and then construct and redirect to your API call. Since your code page is not the API endpoint, Quick Base will redirect unauthenticated users to the login page first.
For example, your new link might look like domain.quickbase.com/db/<dbid>?a=dbpage&pageID=<pageid>¶m1=X¶m2=Y which your code page will then redirect to what you're currently using like domain.quickbase.com/db/<dbid>?act=API_EditRecord&_fid_6=X&_fid_7=Y.
One strategy for extracting query parameters in JavaScript: http://stackoverflow.com/a/979995
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Nathan Hawe
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