However, there are new rivets to install with the kit, which appear to be small tubular rivets and of course they only supply enough to do the job with no errors...

Does anyone have a process on how to install these rivets effectively, without error, and tightly?

I was thinking of using my center-punch to flare out the one side, along with some solid steel backing on the opposite side to keep it tight. If anyone else has a more 'riveting' method, please let me know!
