My question is: Why are you worried about using foundationless comb in honey supers?
What is the reasoning of foundationless frames? I suppose it being cheaper would be one reason. Although any basis of "more natural" would seem useless since brood generally is not raised in honey supers if a honey barrier was established, or an excluder was used.
You mention frames, so I am ruling out the use of TBH. Another style of hive that uses foundationless would be the Warre hive, and that protocol normally calls for constant undersupering, and the destruction of comb when supers are removed.
So I am left thinking you are using a standard hive, running supers, and then for some unknown benefit reasoning that eludes me, are trying to extract foundationless frames.
You can try to slow down, and do this over and over, each time realizing you will lose comb. This is common and does happen.
Why are you not using foundationless in the brood chamber, then using some type of reinforced comb (wired, plastic, etc) in the supers where being foundationless means about absolutely nothing.
Or did you follow someones advice which seemed good at the time, but in practical commonsense makes far less than the ideal situation it was promoted as?