The Trinity Alps Wilderness near the Oregon border is Sierra-like and has self-issuing permits at kiosks.
The Big SEKI Loop is 155 miles but there are shorter variations. You can start at less-busy SEKI trailheads and easily get a permit.
Non-weekend permits are usually available for most Sierra National Forest trailheads.
Sequoia National Forest has several wilderness areas without permits. But it would be challenging to do 100 miles without entering SEKI. Golden Trout Wilderness permits are not in high demand and allow entrance into SEKI. They are obtained from Sequoia National Forest, not rec.gov.
