Are there any languages in which adverbs (in the sense of verb modifiers) inflect to match the verb they modify?
Yes, there are supposed to be some languages that have adverbs that show inflectional agreement with the head verb. I don't know enough to give an overview, but one example seems to be Maori, where adverbs modifying a passive verb take passive marking, and those midifying a nominalized verb take nominalizing marking ("Formal Property Inheritance and Consonant/Zero Alternations in Maori Verbs", by Nicholas Kibre, October 1, 1998; p. 11).
yesterday I went to the storevs.
tomorrow I will go to the storeseems to meet your criteria.