I'm kinda hoping this is because of my +12V wall adapter which really seems to be putting out 14V

Most alternators put out 13.8V anyway so don't expect that to help. Assuming that the current and power are within the regulators specified limits, then you will need to heatsink it.
I don't see much to be gained in dropping volts across series resistors or diodes unless you are close to or exceeding the regulators power rating, in which case you should be able to get safely within spec by doing so. But ultimately, the series diodes/resistors in conjunction with the regulator will be dissipating the same power anyway, and putting the circuit in a plastic box will likely lead to heat buildup with the same eventual result regardless of the presence of any additional diodes or resistors.
So do yourself a favor and use an aluminium box. It's trivial to drill and tap a TO220 mounting position, and the aluminium will heatsink the regulator and dissipate the heat outside of the box. An added benefit is that if you ground the box then you will help reduce any EMI issues.

One other solution is to use a switching regulator, although this will add cost and another potential EMI source.