Yes, cushions (also known as 'bushings') do come in various levels of hardness, and they are the same thing as 'truck inserts', although I've never heard anybody use that particular term (people usually only say: 'cushion' or 'bushing').
You can tell the hardness level of the cushion / bushing by the durometer value that is assigned to it (the higher the number, the harder / firmer the cushion). This hardness-rating scale is the same one that is used for skate wheels.
The biggest issue with getting replacement cushions is getting the correct size to fit your trucks. There are some standard cushion sizes that several different manufacturers use, but there are also some skate manufacturers that use uniquely sized or shaped cushions, meaning that you can only use one specific cushion provided by the manufacturer of that particular skate.
Suregrip is one of the companies that makes standard-sized cushions that can be used with a variety of different makes and model of skate. And in your case they should be guaranteed to fit because your skates are the exact same 'Suregrip' brand.
Heavier people need firmer cushions for stability; this is because the cushions deform more easily under heavy weight, and therefore they become less stable and thus more erratic with regards to steering.
In your situation, I would opt for the Suregrip red (93A hardness) if you weigh 80kg or more (that's about 175 lbs for you yanks). If you weigh less than 70kg then go for the next level down, i.e. the Suregrip purple (85A hardness).
Don't go any softer than that (i.e. yellow or blue) because they'll be far too soft. I weigh 63kg and the Suregrip yellow (79A hardness) are way too soft for me, which means that the even-softer blue (72A) are totally out of the question.
When you buy your cushions, be sure to get the "barrel" version of the cushion and not the "cone" version. This just refers to the shape of the cushion. The Barrel versions are just a straight cylinder shape (which makes them more stable) and the cone-shaped version tapers on one side so that they are kind of pyramid shaped. You can see both shapes of cushion in the photo on the page that you linked in your post.
Cone-shaped cushions are made up of less urethane material than the barrel versions, and so they are more "turny" and feel softer than barrel-shaped equivalents at the same level of hardness. Seeing as you are trying to achieve more stability (to enable easier toe and heel rolls etc.) then getting cone-shaped cushions would be counter-productive, and they may not even fit that well into your trucks (because the link that you provided shows the trucks on your skates to be using barrel-shaped cushions).
Suregrip cushions are pretty good. They inexpensive, as well as being and nice and responsive, so they should do the trick for you (provided that the existing cushions in your skates are not already 93A hardness).
If the new cushions are still causing wobble for you (even after they've been reasonably tightened) then you may need to consider getting skateboard / longboard cushions. Many of them use the same shape and size as Suregrip cushions, so you can look for higher durometer values on skateboard web sites (although it would be a good idea to ask the web site for some cushion measurements before you buy, just to be sure that they'll fit).