Vacuum cleaners move a lot of air volume, but they are about the worst thing you could find for pulling an actual vacuum, probably less effective than sucking the air out through a straw with your mouth.
A refrigerator compressor actually makes a pretty decent vacuum pump. The best I've found are the rotary compressors commonly used in window AC units. Those are about as good as you can get without springing for a real vacuum pump.
Refrigeration service pumps are two-stage vacuum pumps that will go down to a few microns in theory, although the rubber charging hoses and fittings are typically pretty leaky under vacuum. High vacuums are notoriously difficult, very *very* small leaks can spoil the fun and materials that normally seal end up being quite porous. Even stuff that doesn't leak may outgas for days and require steady pumping.
The biggest problem you will have trying to deal with any sort of decent vacuum is finding a suitable chamber to contain it. Pump down to anything resembling a vacuum and you end up with >14 lbs pushing in on every square inch of the chamber, and from this standpoint, the difference between a hand pump for bleeding brakes, testing automotive vac servos and such, and a fancy high vacuum rig with a diffusion or turbomolecular pump is actually very little. Think of how thick and heavy the glass of a CRT is and how violent the implosion can be if it breaks. That is the sort of forces you will be dealing with and most containers you'll find around will simply collapse.
That said, you may not need much of a vacuum to draw the moisture out if you are patient. I have done a bit of potting and casting in epoxy resin and used a plastic bucket with a hand pump to draw just enough vacuum to draw the resin into the nooks & crannies and draw out the air bubbles. Pumping it down to just the point where the sides of the bucket were starting to bulge in was adequate for that task.