Looking for a cushioned chair, new or used, in the $200-250 range,
that extends to the head level and the back reclines.  I'm not looking
for the entire chair to tilt from the seat.  I want the seat to stay
and place and just the back to recline.

This looks like a very nice chair. The details say "seat does not move
when reclining." No price is given, though:

http://www.bakare.co.uk/products/lift-chairs/lift-chair.htm

Thanks, but it's probably in the $500+ range.

The kind of chair you are looking for is called a Morris Chair. They
can range in price from $100.00 to $1000.00 search on morris chair and
shop around.