My max's running voltage is up at 14.3 right after start up, but drops to only 12.7 after a couple of minutes. I'd expect it to stay about 13.5 or so.
I had to replace the battery a couple of weeks ago.
Is my alternator toast?

 

Assuming your new battery is good, connections are clean and the rpms are the same at startup as when you are measuring...yeah, it seems your alternator is getting weak.