I have the Martelli rotating mat. I like it for the large size. It has never wobbled but it could if the two pieces aren't put together to match exactly. I found it at a great price at Walmart online. Put the item in your cart and Amazon will send you notices when price changes. Weird but sometimes the price will drop to over half off one day and be back to regular price the next.
I use the Quilter's Slidlock on all my rulers and it works great on the JT or Stripology.