A linguistic accent versus a grammatical accent.
Unfortunately there isn't a succinct specialized term to differentiate one from the other. Although it is not very elegant, modifying the verb seems straightforward enough. It is almost idiomatic but still not quite. Speech pattern is the closest in practical terms but is awkward to employ as a verb. Delineating the various aspects of what an "accent" is - linguistically - will give enough proper definition to charge the term you select with the meaning you outline.
Dialect, pronunciation, speech pattern, colloquial, idiomatic.. Also making the point of indicating up front that it is NOT meant grammatically.
Even "dialectal accenting/accentuation" works and isn't too awkward.
Homophones can get slippery every once in a while..