Clemcrazy - can you post photos of where they're planted, both a closer-up and a picture from farther away?

Crazy....first off your two varieties...the Gillian..is a type 2 clematis....it blooms on OLD WOOD....and re-blooms on wood produced that season later in summer.
The Perle d'Azure is a type 3 --blooms on new wood after it is cut back in spring.

The Gillian therefore, has to have its wood brought forward---through winter--and blooms on the wood produced the previous season---then re-blooms later in the summer.

I get the impression these are newly planted plants...within the last couple years. If this is the case, then the slow growth may be normal growth for the age of the plants. I'm sure you've heard the old saying...
1st year it sleep......2nd year...it creeps......3rd year it leaps.
In other words, the plants are slow growers and will produce for you when their times comes...you have to be patient.

Both of these varieties are sun lovers....can put up with partial shade....but full sun is best.
You have them growing through another vine....which shades them. Why not try to get them going on their own...then when they prduce the way yo9u want...let them then tangle themselves into another vining shrub.
I have my Gypsy Queen growing up a dead hawthorn tree on my front lawn....but before it died, I had it blooming right after the tree had bloomed. I don't think I was doing the vine any good...competing with the tree's roots for water...anyway....the tree died and the clematis is flourishing.

So you have to do what has to be done to bring most of the Gillian through winter.
It is nice that you are attempting to have two blooms growing together....but one, even with you9r best intentions, are competing for sunlight and since both are sun worshipers, I would suggest you separate them more.

Other than not mulching them so much...clematis can take winter---but what they might suffer from is being given too much protection BEFORE the hard frost...the roots, when confronted by warm soil, tries to grow..and suffer at the hands of cold when it comes. Mulching should be done AFTER a hard frost...then a few boughs of evergreen can help cushion a good snowfall and be comfy for the plants.

I agree with Goren. Also, both GB & pdA are quite vigorous. Jim Fisk would never introduce a plant lacking in vigor & GB was an RHS winner. PdA grows tall like a weed. If relatively newly planted the roots will find water and food and take off, but almost everyone has one or two non performers. Assuming the stems arising from the ground are healthy & the soil is OK by examination-from my experience this is usually a positional problem--semi shade. When moved to full sun good things usually happen. I recently had the same problem with Yukikomachi (among others), advertised as preferring semi shade, only to find it loves sun. Prior to spring PdA should be cut back to the ground, but I would do the same for GB, despite group 2. Don't be concerned about loss of flowers-be concerned about healthy growth, as flowers will follow & this is a good test of how your roots are doing. One other minor thing. I am not a spike fertilizer person, but prefer compost in the ground when planting and fertilizer spread out over the drip line-distal to the root ball, in relative abundance. I think this distributes food diffusely where it needs to be-Good luck.