There is currently no forward momentum on any double-tracking Braintree to Boston. The areas that can be double-tracked around the existing infrastructure are, and the limited additional footage that can be is not sufficient to be worthwhile. There have been plans, such as the 2012 concept, to improve on this but nothing has been advanced by the MBTA.
The Stoughton/NEC routing is preferred as not only 128 but Ruggles (LMA) and Back Bay are much bigger destinations than Braintree or Quincy. But don't be fooled into thinking the NEC has excess capacity. It can certainly handle the same trains better and be more resilient that the Middleboro can, but it won't have the capacity for significant added service until they extend track 3 to Junction and convert the Needham branch to subway.