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Correction- anything west of Alewife on rt 2 is lead pill inducing starting at 530 AM.Since I live in Arlington and do not go into Boston, you'd think I'm pretty much unqualified to offer an opinion.
Regrettably, though, that doesn't stop me.
I think if I were in the OP's shoes, I'd drive Route 2 to somewhere in or near Acton, take the commuter rail into North Station, and walk from there to State Street or wherever.
As others have noted, the drive into Boston on the Pike in an excercise in terminal frustration. Unfortunately, eastbound on Route 2 in the morning anywhere east of Acton is just as bad. Ditto 228, either direction from about Route 3 through the Pike. Which pretty much eliminates the alternatives.