Well I found out I do have an STC for the pressurized mags - ACD Corp STC SE4303NM 4/25/1988 if anyone is interested.
Thanks basloane for your info on flying above FL200. Seems logical that with pressurized mags, the P337 should be good for FL240 at least. I would carry a pony bottle with me in case of cabin pressure loss. The original owner pulled the factory chemical emergency O2 system. I wouldn't mind having it back in service if they still sell the 02 charges.
Pressurized A/C with a ceiling above FL250 require the pilot to have a high altitude endorsement, I wonder if that played into Cessna's thinking.
If I can get up and play in the low 20's, I may have to upgrade my ADS-B.
And that begs the question - What happens when you fly a 978 UAT aircraft above FL180??? Do your wings immediately turn into fireballs? Do controllers screens start flashing red with your tail number??? Curious minds want to know!