Unusual.  Does this engine have a solid state ignition rather than the
magneto
type that most of us wout be more familiar with?

If it is the old standard magneto type, then clearly you will have to
replace the
flywheel.

On the older engines with breaker point magneto ignition, you had to
remove the flywheel to get access to the breaker box to service the
contacts and....

I have hit literally thousands of these flywheels with a regular ball
peen hammer, either on the end of the crank or, (the way they pop off
the best), by hitting them one sharp blow on the counterweight
(opposite the magnet) and NEVER ever destroyed the magnetism.
Thinking back over the years, I have never even seen a Briggs flywheel
with dead magnets.  
Something was radically wrong with your flyweel before you hit the end
of the crankshaft..  

These engines are unfortunately made to be thrown away, and the
time required to set up a puller to do such a basic job would actually
exceed the value of most of the engines..  (tongue in cheek here).

All of the newer ones are solid state ignition anyway, and usually the
cylinder block wears out before there is any ignition problem and
being solid state, servicing the ignition does not require the
flywheel to be removed anyway. (It is all in the coil.. nothing
underneath the flywheel to be serviced except the crankase seal.)

Go to your local mower shop, and ask them to let you look in their
scrap pile for another flywheel or whole engine for that matter, I
used to get them by the dozen for my small engine classes that way.
Most all will run after minor repairs, although with Briggs aluminum
bore engines, most will smoke due to bore wear and they are not
economically  rebuildable. On the plus side, they are not very
expensive to replace with new complete engines either.

Bottom line, you did not harm your flywheel by removing it in the way
that  you did...  

Bob Flumere
rflumere@comcast.net