Good luck. Be sure to post your results!
May not be an issue, but unless you know your personal sensitivity to hypoxia, be very careful above 10,000’.
Many younger healthy persons may be fine up to about 16K (without oxygen), but the signs are NOT obvious. It’s very insidious, creeps up on you with NO notice in most cases. And can be fatal, mostly indirectly by inappropriate pilot input/decisions/actions, including as the top speed eventually decays to equal the stall speed and the stall recovery may be substantially different at the service ceiling from what you are used to.
Also, it’s easy to exceed the Vne on descent, noting that most Vne’s are based on TAS, not IAS.
On the other hand, it’s intriguing, educational and definitely furthers your pilot experience and with safety disclaimers, I encourage anyone interested to learn more about their aircraft’s operational envelope.
Cheers.