Heck, if you only paid $5 for the clem, splurge and spring for a new trellis and plant it on its own!! Not only will you eliminate any conflicting pruning issues but IMO, clematis just look better when planted individually.

I really don't have anywhere in the garden to put a new trellis that gets full sun. Otherwise no brainer would definitely add trellis or teepee.

No room can be created nearby in that same bed by moving a perennial? Or no stiff-stemmed shrubs VdL could sprawl over? Or just do as you originally intended - most of my type twos are pruned by winter weather freezing, so hard pruning it wouldn't be an issue. Whether you think two types look good together is an aesthetic decision that only you can make for your garden. If you like the look (and many folks do) go for it.

Personally, I love to throw things together -- it's a matter of personal taste. If you can plant the root ball a fair distance away so the roots of the plants won't compete too badly, then don't feel bad about making them grow up the same trellis if that's what you feel like doing. A large part of successful (and enjoyable) gardening is experimentation, after all!

fyi, I would hard prune The President, it's scraggly. Hard prune it and give it some alfalfa pellets, compost and Rose Tone and it will grow up much fuller. I often pinch out the tips too to make them shorter and fuller. Once mature, that post isn't going to be big enough for VdL too. You can make a rebar tee pee cheap....with a hose clamp at the top to hold three or four pieces together.

Cutting The President back hard, to 6 inches, will not hurt it. At most it will cause it to bloom a bit later.

Pruning HELPS Clematis, It does not harm them.

surround the post with a wire cage and it will be great. Photo from a private garden I've toured more than once. She has multiple 4 x 4 posts with bird houses on top and wire fencing surrounding covered with Clematis