Thank you for the suggestions!
Two of us went up the Jewel Trail, which was in pretty good condition. We hit snow at around 4,100 feet, but it wasn't all that challenging, even first thing in the morning.
Met two hikers who had come down the Ammonoosuc trail, who told us it was quite icy.
We hiked over to Jefferson, experiencing a fair amount of snow on the Crawford Path. There was still quite a bit of snow on the ridge, and it's extremely important to use lots of sunscreen if you're up on a sunny day.
The hike first to Jefferson and then to Washington was slowed by the snow, requiring some thought about where to put many steps, as the snow either obscured the rocks underneath, or had melted into sometimes large puddles.
Come down the Crawford Path over Washington towards Lakes in the late afternoon under warm sunny skies, the trail was a small river. Massive melt off forced us to walk to walk to the side, and the Ammonoosuc trail was quite tricky, with spots that was still fairly packed down ice, others that was extremely slippery, and others that were awash with melting ice and snow. I would not recommend anyone take this trail even next weekend. It's dangerous. Give it two weeks for nature to take its course and you'll be happier and safer for it. If you must hike it, either bring some sort of microspike, or strap-ons, as there is still a good amount of slippery snow or ice above 4,100 feet.