For New Horizons (and many others):

  http://pdssbn.astro.umd.edu/

Let me know if you need any help.

The hibernation mode of New Horizons has the RTG "cylinder" axis perpendicular to the spin axis, so unless there is asymmetry around the axis of the RTG, I would not expect to see any thermal recoil force. I guess that means we would not expect to see any effect, which neither validates nor invalidates the accepted thermal recoil theory for Pioneer, but it would exclude any "New Physics" explanations (which the planets do already).

You can read quite a bit of detail about NH in the data sets archived to-date in the Planetary Data System http://pds.jpl.nasa.gov/ specifically http://pdssbn.astro.umd.edu/holdings/ look for data set directory names starting with nh- and subdirectories of those named catalog/ and document/.

There is also a lot of geometry information available in the SPICE data set under /http://naif.jpl.nasa.gov/pub/naif/pds/data/nh-j_p_ss-spice-6... e.g. start at aareadme.htm

I said that based on a Wikipedia reference to this paper: http://arxiv.org/abs/0710.5135

Which proposed to do testing in late 2007 through 2008, which I gather didn't happen, no doubt because of the reason you point out.