Hello there,
I had the same issue like you, to link different Google Play account with another Firebase Account. I solved this issue by following steps.
1) Login to your Firebase Account and open your project which you have created.
2) On the top-left, Click on Gear/Setting icon near to "Project Overview" and Click on "Users & Permission".
3) It will open a new tab which will show list of users. On the top, click on "Add+" button and add the "Google Play" account's email-ID and select Role as "Project -> Owner" and click on Save.
4) Now On Mail Account of Google Play account, you will receive a mail to accept invitation, click on "Accept Invite" button link.
5) It will open firebase account in new tab and will show a dialog to add project in your Google Play Account, Check the "I agree.." and click on "Add".
6) It will add Firebase project to your Google Play account and now click on "Project Name".
7) Now Click on "Setting/Gear" icon near "Project Overview" and Click on "Project Settings" and Open tab "Account Linking".
8) Now click on "Link Account" on "Google Play" card.
and it's done.