I find this thread interesting in that I am going through the same thing myself - i.e. my Portuguese floor corker with a 4 jaw plastic jaw system is doing the same thing, i.e. putting a crease in synthetic corks that causes the bottled to leak if you put them on their side. It appears that the jaws don't meet perfectly in a circle to compress the cork without putting a crease in it. The wine supplier shop I bought it from said the problem was well known and his advice was to count to three when I had the cork compressed before inserting the cork and that should help with preventing the crease, but it didn't.
So then I contacted a MoreWine sales rep and asked him why do they say a hand corker will work with synthetic cork and a floor corker will not, he then told me a hand corker would not have enough leverage for synthetic corks so he recommends a floor corker. I told him to read the comments on their website re floor corkers and synthetic corks and he then he came back with the party line that they don't recommend floor corkers with plastic jaws for these corks (W410) but any other floor corker would work, even though that is not what their website states, and includes the one with brass jaws, saying it is not recommended for synthetic corks.. So no help whatsoever, they sound very confused on their own products they sell.
I then contacted a sales rep with the Nomacorc company, and he said first, you need a floor corker to get the compression needed for synthetic corks if you are doing any amount at all, a hand corker will be tiring, and second, to him it does not matter if the floor corker has 3 jaws or 4 jaws, whether plastic or brass, the jaws have to be adjustable, so you can add a shim or something to eliminate all gaps or sharp edges when the jaws compress to form that perfect circle. The key to him was to buy an adjustable compression floor corker, in other words, a jaw system that can be pulled apart and adjusted, even shimmed if necessary.
I then started looking for an adjustable jaws floor corker, I am thinking brass jaws would be better for staying aligned and true, but it did not matter, I could not find anyone who sold anything resembling this.
So I am back at square one, having had no luck in resolving this. I could order replacement plastic jaws for my Portuguese floor corker, but that is really not solving the problem as there is no adjustment as far as I can tell.. There appears to a ton of misinformation out there for a relatively simple problem and a very common problem, and even the Vendors that sell them, like MoreWine seem confused and have no solutions other than recommending a small hand corker with plastic jaws, which makes no sense. Any help on this would be appreciated.