Well done porcelain dental crowns ought to settle in and last for years with no more than minor issues. We always check the fit of any new crown we fit with an X-ray. Your dentist is correct that not all issues with the fit show on X-rays, but it is still the single most useful test to verify the fit. There are no other types of X-rays or MRI's that are helpful or pragmatic.
Often all porcelain crowns are actually bonded. This adhesion process is very technique-sensitive. If the edge of the crown is under the gum line, this can affect the adhesion process. Sometimes the gum irritation is not from a bad fit of the crowns, but from some extra cement left behind. This does often show on an X-ray.
The most practical way to proceed right now is to request an X-ray. Check both the fit of the margin and check for any excess cement. You may need some time with the hygienist and possibly even be numbed so she can do some additional fine cleaning there. In our office our hygienist is trained with the laser. The laser is sometimes an exceptional tool to help improve very fine or delicate gum problems.