My opinions:
Yes, I think you should absolutely give it a go. But like you said in the second part, be just as prepared to not summit as to summit. The mountain will always be there next week, next month, next year. The idea is for you to be around too. Besides, by going, even if you don't summit, you gain valuable experience that will help you on your second bid.
I get the feeling that by your dates, the snow will probably be melted to the point that the switchbacks will be ready for use, and you'll be able to avoid the chute. I have no scientific evidence to back up my feeling, but with the recent heat and TRs, it just seems like three more weeks will be enough to make them usable.
Best way to train is to go out and enjoy the freedom of the hills. Hike, hike and hike. I have a small child at home that requires a lot of attention and can not hike, so I spent a lot of time in the gym. I'd max out the incline on the treadmill and walk at a rapid pace. Get on the stair climber. Ride the bikes. Those were my big three when I couldn't hike this year to prepare. In my opinion, nothing in a gym can prepare you for hiking better than hiking itself. But the gym will still definitely help.
