I think someone finally found the right terminology, and simultaneously set my mind my at ease. He said:
"You're writing in past tense (third person) and using participle phrases. Participle phrases are not incompatible with past tense; they're used all the time. There's nothing wrong with this, in moderation, like anything else. If the three sentences you quoted above were consecutive, it would ring repetitious in my ear. I suppose I could nitpick a few other items, but the point is that the structure is perfectly fine."