Leave them outside in a spot where they get no direct sun and they should root in less than a month. If you want to do it indoors, bottom heat would probably speed the process a tad. I've tried rooting climbing h. and have been very unsuccessful. Takes more hovering than i have patience for. I'm sick about your deer damage.
Deer know if the dogs are confined in any way.
Have resigned self to the fact that I need to erect that deer netting fencing to a height of at least 10 feet all around the entire perimeter of my garden area. Is going to be one helluva chore, but I think it's the only chance I have to grow what I want with any peace of mind. Non blooming is caused by either pruning at the wrong time, cold damage to flower buds or, just possibly, too much fertilizing with high nitrogen fertilizer. I would bet, however, that you've got one of the H. macrophylla cultivars and are either pruning it too much in early spring or late winter or the flower buds are getting damaged by frost. If your shrub is exposed to the full brunt of winter winds, that can make a difference.