Hi Lane,
Thank you for your feedback on the table search bar and the issues your team is running into when using it with the current set up. There isn't currently an option native to disable that search behavior on a table/report based search so that it doesn't default to searching when it senses that a user has stopped typing. For some heavily used reports and searching a dashboard search widget set to that table or report behaves a bit differently and doesn't search until the user hits enter, which can help with a specific report that you run into this issue regularly with in the short term.
I would suggest also submitting your feedback from your experience in our User Voice feedback platform. it is a customer facing feedback forum that our development team use to explore customer suggestions. It is a good place to get visibility for your issue as other users can vote for your issues to show their support giving our Product Development team an idea of how many other users would like to see a change to the search behavior above and beyond our internal feedback. It can be most easily accessed from the My Apps page in Quick Base by clicking on the orange Feedback tab or at
http://quickbase.uservoice.com. I would also suggest if you do end up putting your feedback in our User Voice forum that you link it here so that those following this conversation can add their vote. Thank you very much for your time today.