  The post-Newtonian approximation is still the most widely used approach to
obtaining explicit solutions in general relativity, especially for the
relativistic two-body problem with arbitrary mass ratio. Within many of its
applications, it is often required to use a regularization procedure. Though
frequently misunderstood, the regularization is essential for waveform
generation without reference to the internal structure of orbiting bodies. In
recent years, direct comparison with the self-force approach, constructed
specifically for highly relativistic particles in the extreme mass ratio limit,
has enabled preliminary confirmation of the foundations of both computational
methods, including their very independent regularization procedures, with high
numerical precision. In this paper, we build upon earlier work to carry this
comparison still further, by examining next-to-next-to-leading order
contributions beyond the half integral 5.5PN conservative effect, which arise
from terms to cubic and higher orders in the metric and its multipole moments,
thus extending scrutiny of the post-Newtonian methods to one of the highest
orders yet achieved. We do this by explicitly constructing tail-of-tail terms
at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in
the small mass ratio limit, and comparing directly with numerically and
analytically computed terms in the self-force approach, obtained using
solutions for metric perturbations in the Schwarzschild space-time, and a
combination of exact series representations possibly with more typical PN
expansions. While self-force results may be relativistic but with restricted
mass ratio, our methods, valid primarily in the weak-field slowly-moving
regime, are nevertheless in principle applicable for arbitrary mass ratios.
