As a junior who also knew that I wanted to apply directly to PhD programs the following fall, I was able to persuade my advisor to let me enroll in the two semester research seminar/thesis writing sequence in my junior year so I would have the thesis to use as a writing sample. This worked out for me, so I definitely think you should go ahead and start the honors seminar in the spring if it is offered in the spring semester at your university.
As far as revising and preparing a writing sample from an honors thesis... I was fortunate to have a bit more time for this than most applicants applying directly from undergrad. However, I will second what Neist said about working closely with your advisor to do multiple revisions. I also asked members of my thesis committee to read over some revisions and make suggestions on certain points. They will already know your thesis, so this probably should not feel like too much of an imposition on their time. Or, you could ask your letter of recommendation writers.
One other thing to keep in mind, and that you probably already know, is that many (though by no means all) PhD programs will ask for a writing sample of 20-25 pages rather than accepting your entire thesis. I don't know how lengthy an honors thesis typically is at your instituition, but for me that meant I submitted a few well-polished chapters from my thesis rather than the entire thing. It could be very useful to go ahead and look at the application instructions for each program where you intend to apply, and note how many pages they will accept for a writing sample. This could help as you are planning thesis chapters and thinking about organization, etc.