I thought I had recently written about stamping on glossy cardstock....but I sure can't find it so please forgive if this all sounds too familiar.
Most stampers do find stamping on glossy a little tricky and definitely different from regular cardstock. Personally I don't like putting the paper on top of the stamp because I often bump the edge of it and smear the ink before beginning to stamp. As well I am slow deliberate stamper so it takes me too long to eyeball the paper over the stamp and by the time I am done rubbing the stamp the ink is too dry for a good image. And then there becomes the whole issue of how do I pull the paper straight off the stamp that it is sticking to. All of that is to say...we have some individual difference so some this is a learning process of what works best for you.
I find when a stamp sticks to paper it is generally due to a ink issue...either the ink pad needs re-inking or it has dried too much during the stamping process.
Solvent inks like Stazon dry much quicker on both inkpads and on stamps. If the stamp pad is really juicy some stampers leave the stamp on the paper for approx 3 seconds before lifting it straight up. But if the stamp is left too long for the amount of ink on the stamp that could be one reason for gray tones appearing. Stazon ink evaporates quickly and that is why they come with the clear plastic inner line. They are annoying to take on and off and so you will find some suggestions on the Internet to stick them to the lid with a glue dot. This however causes the lid to not seat against the base properly and makes the cover far less efficient. Since I do not use my Stazon pads regularly I often find it necessary to reink my Stazon inkpads when I do pull them out.
I find it most helpful to stand when stamping on glossy. Standing gives me a better range of motion to lower the stamp straight down on the paper and most importantly to lift the stamp straight up in the air when finished. If it feels like the stamp is sticking standing makes it easier for me to hold the paper firmly with one hand while stamping with the other.
It indeed takes a little time and practice but certainly worth the effort. Speak up if you continue to have issues for there is certainly lots of other experience here who may be able to offer other suggestions.
...Jan