Teeth Feel a Bit Loose After 6 Crowns to Top Front Teeth, Normal?

I would be very concerned that there is a traumatic occlusion.  The neuromuscular system will try to avoid nociceptive inputs and this could result in TMJ disorders and/or headaches.  

It is also possible that you are developing a bruxism habit or that increased crown length is allowing more torque from previously existing condition.  If the teeth are loosest in the AM this could be cured by nocturnal bruxism appliance.

I assume that there are no underlying issues such as bone loss from periodontal disease.

If the crowns were recently placed and the contacts are all in porcelain then there is ususally a period as the contacts  are "settling in" that you may feel the sensation of movement. Your teeth are always in a constant state of moving very slightly but since they have been contacting each other naturally you do not feel the movement. new porcelain contacts especially if they are tight may give a bit of a scratching feel when they are first inserted. The obvious signs of tooth grinding or loose teeth from traumatic occlusion would be immediately noticable by the dentist and you would feel the damage you would be causing with your bruxism.

If these teeth were not loose before the crowns were done, then something has changed and another discussion and visit to your dentist would be wise.  A high bite or periodontal problems may be the cause.  Sometimes a protective splint can be made if there is a grinding habit or another bite related issue.  If you are still uncomfortable with your dentist's recommendation or answer, it is OK to get a second opinion as you probably spent a lot on your crowns.  Good luck!