How do I get around the 2,500 limit on reports referencing a larger sheet?

I have a sheet which represents our entire workforce. I have setup a check-in report for our clinic to check in staff arriving for a vaccination. We have just over 3,400 records in our master sheet. We have them doing a look-up to check people in. We do a basic Ctrl-F. The challenge we have is that the report lists only 2500 records so we only go up to alphabet 'R'.

I've set some filters to try to circumvent the limitation, but this isn't a perfect solution and I am looking for alternative methods to operationalize this. There are pieces of my main sheet I don't want everyone to see, so the report seemed like the ideal option. If I hide fields, it breaks some of the reference ranges.

Any ideas? Thanks! Lisa