The fee to enter SEKI is now $20 for 7 days, $30 for a yearly pass.
Also, you might point out that Florence Peak actually sits on the boundary of Sequoia National Park and Sequoia National Forest. You can hike to it from the National Forest side as well, though the approach is definitely longer.
"After the first glass, you see things as you wish they were. After the second, you see things as they are not. Finally, you see things as they really are, which is the most horrible thing in the world."
--Oscar Wilde on Absinthe