The recent discovery of a population of eccentric (e ~ 0.1) millisecond
pulsar (MSP) binaries with low-mass white dwarf companions in the Galactic
field represents a challenge to evolutionary models that explain MSP formation
as recycling: all such models predict that the orbits become highly
circularised during a long period of accretion. The members of this new
population exhibit remarkably similar properties (orbital periods,
eccentricities, companion masses, spin periods) and several models have been
put forward that suggest a common formation channel. In this work we present
the results of an extensive timing campaign focusing on one member of this new
population, PSR J1946+3417. Through measurement of the both the advance of
periastron and Shapiro delay for this system, we determine the mass of the
pulsar, companion and the inclination of the orbit to be 1.828(22) Msun,
0.2656(19) Msun and 76.4(6) , under the assumption that general relativity is
the true description of gravity. Notably, this is the third highest mass
measured for any pulsar. Using these masses and the astrometric properties of
PSR J1946+3417 we examine three proposed formation channels for eccentric MSP
binaries. While our results are consistent with eccentricity growth driven by a
circumbinary disk or neutron star to strange star phase transition, we rule out
rotationally delayed accretion-induced collapse as the mechanism responsible
for the configuration of the PSR J1946+3417 system.