The Canyon is simple to navigate with Foreflight, which shows the VFR corridors as you zoom in. I always carry the printed Canyon chart and an antique 'VFR Guide' that has B&W photos from the POV of the corridor entry and exit points. Flight following is available at these levels and will warn of opposite corridor traffic. The tour traffic is far below when you are flying the corridors.
I doubt the corridor altitudes will be any problem to a TBM 750! It's quite right about the early morning departures in the summer, although DA isn't the only problem - it gets very bumpy indeed during the day. Especially in August, you can expect afternoon thunderstorms as well.
An interesting routing out of Vegas is along the Western end of Canyon just above the Special Rules Area (8000', steps up to 9000') as far east as Bar Ten Ranch (1Z1), then N out of the SFRA and East along the Arizona Strip Country with a possible landing at highly scenic Kanab (KNB). Then a Southbound crossing through the Fossil Corridor and back Northbound again through the Dragon corridor on more or less a direct track to Page, Arizona (PGA). At the end of that, your passengers (if you have them) will have seen enough Canyon for the day! And in the morning, there's Monument Valley...
I don't recommend Grand Canyon West and it's $100 landing fee, although some people enjoy the Skywalk...
How do I know? Well, I fly from Prescott, just 80mi S of the Canyon, so almost every trip involves crossing it somewhere!