I have found another reference that seems to provide support for a role for the ΔFosB protein in the levodopa LDR.

"These data suggest that the L-DOPA-induced ΔFosB-like proteins have ongoing transcriptional​ effects for more than 2 weeks after treatment discontinuation.​ Such effects may account, at least in part, for the long-lasting effects on ​brainfunction produced by L-DOPA treatment."

Time course of striatal ΔFosB-like immunoreactivity and prodynorphin mRNA levels after discontinuation of chronic dopaminomimetic treatment (2003):

[PDF] Time course of striatal DeltaFosB-like immunoreactivity and prodynorphin mRNA levels after discontinuation of chronic dopaminomimetic treatment. - Semantic Scholar

I've also found an open access "Author Version" of johnt's second reference (see above):

Inferring the long duration response to levodopa in Parkinson's disease - Open Access Repository