Owning a P337H, going "strapless" is not an option for me.
However, in my previous life as a Beechcraft owner, every model I owned from Bonanzas, Travel Airs, Twin Bonanzas, and Barons ALL had their factory center strap removed and replaced with D'Shannon one-piece windshields.
The only question was what thickness and tint color I desired. There was never an issue of airworthiness.
I once had a birdstrike on the Baron one-piece windshield whilst on approach to FXE (Fort Lauderdale Executive) by a very large seagull. It cracked the windshield, but did not penetrate.
My two cents.