  High statistics results for the isovector momentum fraction, $\langle x
\rangle_{u-d}$, helicity moment, $\langle x \rangle_{\Delta u-\Delta d}$, and
the transversity moment, $\langle x\rangle_{\delta u-\delta d}$, of the nucleon
are presented using seven ensembles of gauge configurations generated by the
JLab/W&M/LANL/MIT collaborations using $2+1$-flavors of dynamical Wilson-clover
quarks. Attention is given to understanding and controlling the contributions
of excited states. The final results are obtained using a simultaneous fit in
the lattice spacing $a$, pion mass $M_\pi$ and the finite volume parameter
$M_\pi L$ keeping leading order corrections. The data show no significant
dependence on the lattice spacing and some evidence for finite-volume
corrections. The main variation is with $M_\pi$, whose magnitude depends on the
mass gap of the first excited state used in the analysis. Our final results, in
the $\overline{\rm MS}$ scheme at 2 GeV, are $\langle x \rangle_{u-d} =
0.160(16)(20)$, $\langle x \rangle_{\Delta u-\Delta d} = 0.192(13)(20)$ and
$\langle x \rangle_{\delta u-\delta d} = 0.215(17)(20)$, where the first error
is the overall analysis uncertainty assuming excited-state contributions have
been removed, and the second is an additional systematic uncertainty due to
possible residual excited-state contributions. These results are consistent
with other recent lattice calculations and phenomenological global fit values.
