How can I get unblocked from Apple CheckCoverage?
I would ask you Apple sales person to get you an account on Apple Business Manager. That one account will unlock all manner of goodness. You can then apply for customer seeding programs, get global service accounts to check serials and more. 


https://business.apple.com/


If you don’t have a business contact, just estimate how many Macs and Apple products you manage and call sales 1-800-MY-APPLE and ask for a referral or walk into an Apple Store and ask for the business team. 

Your contact will then go to bat and either get you trained on the new tools or cleared from the abuse filter for the web page you triggered.