This may have been suggested before, but my wife has a rather
clever machine called a "Big Shot" made by Sizzix (Google 'Big shot').
It is made to cut out paper and cardboard shapes for crafters --
scrap booking and card making -- but I feel it would almost certainly
cut felt as well.

The 'dies' seem to cut quite complex shapes but are relatively simple:
a cutting edge fixed to a metal base and buried in foam rubber, which
protects the die and holds the paper in place as the cutter is fed
through the rollers of the machine.

It seems very simple and is easy to obtain either new or on eBay.
So would it be possible for someone (an engineer?) to design and make
a die, or even a set of dies to cut out the most popular gaskets?

Suggestion 2:-

There is also a computer driven crafters die-cutter called the Xyron
Wishblade (Google Xyron Wishblade).  This apparently allows you to
design a shape on your computer and then cut it out.  I don't have
access to one of these but suspect it would only be suitable for
cutting paper gaskets, and then possibly only in small quantities, but
with a good scanner the possibilities for short runs seem endless.

Robert Kissick