*Bites nails*
I don't think you should do a thing on the request side for now. You have an inherent grace period of a few weeks. USE IT! You've indicated that you work quickly, and that seems to work well for you, so go with your strengths. For now.
Few agents will come looking for the book in the next few weeks. I've had it happen, and have seen it happen, but it's not the norm. Most are overwhelmed by queries and requested materials. You've got a little time to do this right.
So, throw your opening up on SYW, get friends to read, make all the revisions you've already determined need to be made. But send those agents the best possible version of your work possible.
BUT WITH A CAVIAT: If the whole book is unready, then please go with what Cricket18 and Trocodero recommended. If you just need a little time to tweak, you can buy yourself a bit. It really just depends on what you want out there in a few weeks time. I wouldn't give it much more than that, though, and I'd be VERY careful about pulling the "I'm revising" card. It sounds respectable, and it's preferable to sending out subpar work, but it still casts a dubious light on the book...