Cross country from 60 Lakes to Rae Lakes?

I'm looking at the topo map with a trail showing going north into the 60 Lake Basin, northwest of Kearsarge Pass, and also the JMT going north past Rae Lakes. Wondering if anyone has gone cross country between the two areas? The topo map suggests it's possible if one continues north in the 60 Lake Basin far enough. If you've done it, how tricky would this be? I'm AGS' wife, so we have off-trail experience aplenty. Thanks.

If I follow what you are asking, the answer is yes. We did it by entering 60 Lakes Basin over Rae Col after crossing Glenn Pass and exiting the basin by following the outlet creek of the northern most lake-let in the basin down to the unnamed lake north of Arrowhead (or NW of Dollar). This section is a bit steep but nothing beyond some class 2 scrambling. From there, we followed the inlet creek of the unnamed lake up to Arrowhead Lake. There is actually an old trail that runs directly alongside this creek with switchbacks up to Arrowhead. The switchbacks looked like they had been engineered, so this was at one time probably more than just a use trail. We did not go north from this unnamed lake, but the old trail probably head north to connect with the JMT. You could also exit 60 Lakes Basin by going through "Basin Notch" just to the west of Arrowhead. I think that is the more "traditional" cross country route. If you want, I probably have pics of the cross country sections we did if you want to see them.
BTW, take the time to visit all the little lakes in the basin. Most are quite nice, especially the ones just below Mount Clarence King.

I've done a loop using that trail and returning cross country, here's the route I followed: https://www.strava.com/activities/1840080799 We came over the saddle about even with Arrowhead Lake. There was one section that was a bit tricky to downclimb, probably class 3, but you could probably get around it without too much effort.