The problem for me isn't Miller, it's the MLE. I think it'd be much better spent on a quality wing.
Yes, Perk is out, but he won't be out the entire season. In the meantime, we could get by with less at the 4/5 spot. Quite frankly, a rotation of KG, BBD, Shelden, and Scal could still win this team 55-60 regular season games if everyone else is healthy (not saying that we should re-sign the last two, just an example). So I don't see why overreacting to the Perk injury is all that important. We will make the playoffs with or without him, so it's really just a matter of him coming back by then.
And once he is back, we really will only need 10 mpg or so from a backup, because BBD is ready for bigger minutes.
If we do go with Miller and don't have the MLE, we better hope that Tony Allen is even better next year and that Avery Bradley is NBA ready. We desperately need some players to take pressure off of Pierce and Allen.