Can I actually get a crown that feels more like how my tooth did?

Porcelain crowns made well depends on the preparation of the underlying tooth by the dentist and also the skill of the ceramist. Good thing is that you like the cosmetic of the front, ask your dentist if he can reshape AND polish the back surface. Some type of crowns such as zerconia or Emax are very hard to polish after adjustment. He knows if there is room for porcelain to do that, or not. If for any reason he can not and still bothers you in couple of weeks then unfortunately, you may have to redo the new porcelain crown.

The back part of the crown on front teeth usually feels kind of bulky. It gives the crown a little more strength if it is thicker. Thickness can't be added to the front because it would look weird. It could be reshaped a bit, but I would give it a week or two and see if you can get used to the feeling before adjusting the crown.

See if your dentist can recontour the back of the tooth some without compromising the strength. Often times new crowns will feel bulky at first.

Of course you can.   The lab made the crown too thick for one of the reasons.
1. Underpreparation of the tooth by the dentist. 
2 .poor me choice of materials by the dentist and lab.  They could have used a material that could be made thinner.
3.The dentist just does not understand why you are concerned. He made the temporary thin so he can make the permanent thin as well.