I don't know about 'ready cut' strips, (never used them) but I know it works with the fabric in the kit , which is a 50x50 weave high-quality fabric, with just the right amiount of adhesive. Sometimes certain makes have too much adhesive on the back of the strip, and this can cause an opaque look.
It is easy to cut your own strips and in my opinion less wasteful. So I would stick to the system and see how you go with that. It is also quicker if you cut all 10 strips at once and curve off all ten ends at once with your scissors. All that picking up and putting down wastes tonnes of time.
When you apply the BOND, work as you say you are doing, slowly and carefully, and rather than using a painting stroke, sort of pat or 'stipple' the BOND into the fabric as you move down the nail, so that you know that all the little perforations (reminds me of that Tea bag advert) get filled with BOND. When dry, do it again. In my opinion 2 coats work best for me.
Let us know how you get on. It should be crystal clear every time.