Rebuilding toilet tank

We've had such a problem with a sticking flap, running on in the toilet, the hose leading to inlet popping off and spraying water, that we decided to replace all of the parts in the tank. We bought a Korky universal kit. After much work my husband got all of the old parts off and attached the flush valve. When he went to attach the tank to the bowl, the sponge gasket was way too large to fit into the bowl opening and that made the tank unable to sit on the bowl. There is a significant space between the two and the tank wobbles and shakes really bad. The hole opening in the top of the bowl is 2 1/2". Is there some type of gasket that goes where that sponge is supposed to go that will allow the tank to sit down on the bowl like it used to? Before we took it apart, it sat flush (no pun intended) on the top on the bowl. It just seems so unstable to leave it like it is. I'm not sure how old the toilet is, but we've lived here 18 years and it was here when we moved in.

Thats the trouble with universal kits...
As you found out they are not universal.
It sounds like you have a close coupled toilet.
What kind is it? Can you post a name and any model #'s you can find on the tank or the bowl?

tank

You should be able to tighten the tank so there is minimal movement. Sometimes some movement is desirable to prevent stress on the tank which can crack it.