We are not aware of any any specific rule about use of adverbs in relation to participles.
Adverbs have easy access in the sentences. Adverbs, or for that matter adverbials make room for themselves at the beginning, in the middle or at the end of sentences. No other part of speech has as much liberty as has an adverb.The references that are made in this poster apply to the placement of adverbs in general, not particularly in relation to participles.
PARTICIPLES are verb-adjectives. For this unique dual nature, participles, according sentence-spcific demand, somewhere gains in adjectivity and at places,relegates it to verbal qualities. As:
•A rolling stone gathers no moss.(adj. Predominance)
•Hearing the noise the child woke up.(verb predominance).
To our mind, there must not be any difficulty as regards to the placement of adverb.
Generally adverbs of manner are placed after intransitive verb or after the object of the transitive verb and when adverb modifies an adjective,the adverb comes before it. Modifying adverbs may be viewed in this light.
In all the examples, "driving" is the participle from "DRIVE"-- a verb of course transitive,used intransitively. Hence,it invites so much of comments.
So far as I am concerned, none of the four examples is grammatically wrong. However, it is left to the learned moderators to accept the right one lest we may land on such a situation:
I saw a dead cow slowly walking on the field.