detach the ISR and process the results.
Don't do that just disable the interrupts.
One possibility is the RC debounce circuit is not adequate,
Yes that is what is causing you problems reed switches bounce more than a bucket full of frogs.
Use the millis timer so that you only update your counter after a specific time. The millis timer will not advance in an interrupt routine but it will be readable and you can store the results when you get an interrupt and ensure you don't count again until a certain time as passed.