Re: Trip to Livingston
This is definitely a bad idea. I have never seen anyone float/fish the Yellowstone in anything less than a Class III-rated pontoon and only even see canoes in a couple short sections. In mid-July the river will certainly be fishing well, but it will still be up to the edges of the bushes with few gravel bars exposed for bank fishing, lots of weird/turbulent eddies, and submerged rocks ready to rip the guts out of a boat that doesn't have durable tubes. This is especially true east of Livingston where there's a lot of weird small channels, islands, rock bars, and sudden changes of direction, even if the rapids are generally smaller.
For a fun-only drift, you could do Gray Owl to Mallard's Rest in Paradise Valley, but I wouldn't try to fish out of a boat like yours.
For a few hours' fishing around Livingston, you will be much better off hitting up a couple of the smaller creeks, wade-fishing a few stretches of the Yellowstone that do have accessible banks, or heading up into YNP.