Steve, it must be a fairly common problem on the 360s.  Mine had the same issue
last year an annual time (at around 340 hours).  Also, same response from
Lancair.  My A&P ended up fabricating a new one using the old one as a
template.  He also beefed it up for additional support.  I was unable to find
anyone with an extra at that time.  Good luck.
Matt McManus
LNC2 360

Quoting Steve & Kelly Rosenzweig <krosenzweig@socal.rr.com>:

...on my 360 MKII and found the spinner backplate was terribly cracked...