I haven't been up in that area this year so I can't comment on conditions, but climbing both LeConte and Mallory on the same day after camping at Meysan Lake is very doable.

I was up to 10.5k wed night in running shoes with no problem. Small snow fields were soft even at 7pm. My guess is that even at altitude things have got to be soft during the day. I would not worry about both crampons and axe. I would probably just take an axe, or nothing.