I did south Morgan over a month ago, the snow was easily avoidable. However the axe allowed me to use a steep snowy chute to hasten my decent with a glissade. Don't know if the snow would still permit that now though.
I hiked Mt. Morgan (south) in July with none of the snow travel equipment you mentioned. It was fine. You could even avoid the snow if you wanted to, but I ended up glissading on some sections with just hiking poles. I imagine there would be a lot less snow up there now than there was when I was up there. Have fun - it's quite a view.
So, definitely clear all the way to the summit. Thunderstorms were more of a problem. Turned around a few hundred feet from the top; about 10min later it was snowing. Looked like it was the right decision.