This can sometimes happen when acceleration is babied at low speeds. Take it on the freeway and while merging, floor it a couple of times (through the kickplate) to redline.
Check with the dealer again to see what your cost would be with Mazda contributing to it. Sometimes a dealer will bill differently for a 100% customer pays job vs a partial Mazda payment job
You don't have to contact multiple dealers. One will be able to access the details of the work done at any other Mazda dealer. They may want to confirm that you are the owner
When it's oil change time, just take it to a dealer and ask that when they do the multi-point inspection if they could also check for any leaks or cylinder head cracks. It's still under the powertrain warranty and anything found will be covered
Ask the seller if you can take it to get inspected. Then take it to a Mazda dealer for a used car inspection. Depending on labor rates in your area, should run about $150