I had the same problem when I was a PhD student. I spend several days cleaning it, drying it, greasing it, putting on brand new tubing etc, all in time for our supervisor's return from an overseas trip and his military laboratory inspection. Moments before he entered the laboratory I inserted the last piece of tubing on the 6th valve of my manifold, at which point the valve snapped and blood pressure rose to brainstroke alert levels.
To answer your question, unfortunately you would have to use a base bath from my experience. You will have to make a larger bath which can fit your manifold in, but be sure to properly assess the risks and to discuss this with your Health and Safety technician BEFORE you begin making the base. I would recommend using isopropyl alcohol instead of acetone, as it is less volatile and easier to contain. Also, use a mineral base - not ammonia. Be absolutely certain that you removed all plastic pieces before you immerse the manifold into the bath, and make sure you do not lose any pieces that you separate from the manifold during the cleaning process.
Last but not least - do not leave the manifold in the bath for an extended period of time. If the glass wears thin during the cleaning process your manifold may break under strong vacuum. Use a long wire brush (there should be some available from chemical suppliers) to clean up inaccessible bits.
Athan (PS - drop me an email if you need more specific advice or you have any concerns about putting your manifold together)