  Models of stellar structure and evolution can be constrained by measuring
accurate parameters of detached eclipsing binaries in open clusters. Multiple
binary stars provide the means to determine helium abundances in these old
stellar systems, and in turn, to improve estimates of their age. In the first
paper of this series, we demonstrated how measurements of multiple eclipsing
binaries in the old open cluster NGC6791 sets tighter constraints on the
properties of stellar models than has previously been possible, thereby
potentially improving both the accuracy and precision of the cluster age. Here
we add additional constraints and perform an extensive model comparison to
determine the best estimates of the cluster age and helium content, employing
as many observational constraints as possible. We improve our photometry and
correct empirically for differential reddening effects. We then perform an
extensive comparison of the CMDs and eclipsing binary measurements to Victoria
and DSEP isochrones to estimate cluster parameters. We also reanalyse a
spectrum of the star 2-17 to improve [Fe/H] constraints. We find a best
estimate of the age of ~8.3 Gyr while demonstrating that remaining age
uncertainty is dominated by uncertainties in the CNO abundances. The helium
mass fraction is well constrained at Y = 0.30 \pm 0.01 resulting in dY/dZ ~ 1.4
assuming that such a relation exists. During the analysis we firmly identify
blue straggler stars, including the star 2-17, and find indications for the
presence of their evolved counterparts. Our analysis supports the RGB mass-loss
found from asteroseismology and we determine precisely the absolute mass of
stars on the lower RGB, 1.15\pm0.02Msun. This will be an important consistency
check for the detailed asteroseismology of cluster stars.
