Ric-
I don't know what woods you have available locally...
If you can get ash (preferably a straight-grained piece), it bends well.
Yellow cedar is a good bending wood, but not available everywhere.
Basswood is 'reasonable' for bending.
Mahogany can bend well also.

It's a 'long way round and round' if you have to use very thin strips.

Using a layer (or two) of plywood makes a lot of sense to me - balancing the expense (and waste) with plywood vs the time and glue for laminating the whole lip..but it's a hobby, right? ...we're mostly not in the production game here....
;-)