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The motion of a small compact object (SCO) in a background spacetime isinvestigated further in a class of model nonlinear scalar field theories havinga perturbative structure analogous to the General Relativistic description ofextreme mass ratio inspirals (EMRIs). We derive regular expressions for thescalar perturbations generated by the SCO's motion valid through third order in$\epsilon$, the size of the SCO to the background curvature length scale. Ourexpressions are compared to those calculated through second order in $\epsilon$by Rosenthal in [E. Rosenthal, CQG 22, S859 (2005)] and found to agree but ourprocedure for regularizing the scalar perturbations is considerably simpler.Following the Detweiler-Whiting (DW) scheme, we use our regular expressions forthe field and derive the regular self-force corrections through third order. Wefind agreement with our previous derivation based on a variational principle ofan effective action for the worldline associated with the SCO thusdemonstrating the internal consistency of our formalism. This also explicitlydemonstrates that the DW decomposition of Green's functions is a valid andpractical method of self force computation at higher orders in perturbationtheory and, as we show in an appendix, at all orders in perturbation theory.Finally, we identify a master source from which all other physically relevantquantities are derivable. Knowing the master source perturbatively allows oneto construct the waveform measured by an observer, the regular part of thefield on the worldline, the regular part of the self force, and orbitalquantities such as shifts of the innermost stable circular orbit, etc. Theexistence of a master source together with the regularization methodsimplemented in this series should be indispensable for derivations ofhigher-order gravitational self force corrections.

A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source