A better solution would be to only allow a bug to be reported once per quarter, or once per version of the software. If someone finds a bug in v1.0 that's fixed in v1.1, then someone (even the same person) should be able to report the same bug in a different place in v1.1. That's an incentive for companies to use the report to secure the whole app rather than just fixing the reported issue.
But you might have the same vulnerability found in several different places. Reports should really only be considered duplicates if the fix to one automatically fixes the other also. Your bug found in multiple locations might happen to be set up that way -- or it might not.
This exact problem occurs frequently when a company with a bounty program makes an acquisition and brings the new software into scope for the program. The acquired code is often full of relatively easy-to-find, high-impact bugs. What I've seen people do in this case is open the scope, accept a certain number of reports, and then suspend eligibility for that software for a certain period of time.
This would look like "we've had a lot of similar bugs filed against company-we-acquired.com, and we're taking that domain out of scope for X weeks while we work on it."
By the way, the security bounty should be mandatory to display to customers. It’s like saying “We don’t value the sum of all your data of all customers to more than $1750”.