This conversation is sounding kind of funny because the Abelia and Kolkwitzia genera no longer exist. They're both part of the Linnaea genus now (except for a few Abelias that are now classified as Zabelias). Anyway, here are some closeups of the leaves of my mystery plant (at the top) and a Linnaea amabilis (formerly known as Kolkwitzia amabilis).
Neither is hairy on the underside. The leaves of the mystery shrub are smaller, but could that be due to its relative youth? The L. amabilis at the bottom in the two photos is about 15 or 20 years older. Also, the L. amabilis bloomed a couple of months ago and was pruned afterward, whereas the mystery shrub was too young to bloom and therefore was not pruned. That might be the reason it's showing reddish new growth, in contrast to the older shrub.
Top of foliage
Underside of foliage