Several years ago we went in from the west via Pyra-Queen Col, a truly horrid crossing. The west side consists of several hundred feet of scree, steepening towards the top. It is under class 3, but with a full pack, it is unfun. The easier part is the east side, which consists of several hundred yards of talus-hopping. We exited the basin to the north, I believe, via a somewhat convoluted route that I don't remember very well. It's described in Secor's book, along with Pyra-Queen Col.
With that said, spending a few days at Kaweah Basin was well worth the effort getting there.