I received some good responses to my post on my Clematis vines:

Yes, tree roots are a problem for clematis in my opinion. They rob so much of the moisture and nutrients that clematis may well struggle.
Your Ville de Lyons are only babies still, and will take several years to reach normal size. Wayside sells ‘liner plants’ at a premium price. This is rather unfair to unsuspecting consumers in my opinion.
Ville de Lyon is a group 3, hard prune type, and I simply shake my head when I see well known nurseries make the mistake of incorrect pruning groups on their web site and labels. It goes to show that they don’t really know or care much about the clematis they sell !
Fertilizing your clematis is really easy. Just top dress every season with manure and some rose food and perhaps bone-meal if you have it. About mid season you can repeat the rose food.
The soil alkalinity shouldn’t be any problem. Clematis do well in just about any soil if they have water and nutrients. My best advice is to water, water, water and top dress with manure and rose food. Your plants will eventually take hold and shower you with flowers once they finally grow up.
Ville de Lyon has a beautiful color and it is one of my favorites with it’s striking and unbelievable rosy red/pink color ! A real winner.
Suzy

Here’s another from the same lady, in response to my follow-up question about whether I should really leave them where they are or dig them up and move them:

Stevation, I would be inclined to leave your clematis where they are for a few years to see if they can overcome the competition from the tree roots, but I would give them lots of extra water and a good top-dressing of manure and fertilizer for added insurance.