I agree with Kimberly. WD40 is good for friction points, but not as a cleaning agent.
I have restored several presses. Taking it apart is not a bad thing at all. You can clean the pieces with a good degreaser like simple green or greased lightning. Use a fine steel wool with some of that 30 weight oil to buff off any rusted spots. If you need new paint, degrease again and paint with a Rustoleum, like matte black.
When you clean really well, it is very important to re-oil the various joints before putting it back into use. For most spots the 30 weight oil will work great. Look for the lubrication holes, sometimes painted red, above a joint, and squirt the oil in. I like to use a dab lithium grease for the ink disc post and collar, since that spins a lot during the run, and the grease doesn’t break down as fast as oil.
A Craftsman is a very similar pull-lever platen press model to a Chandler & Price. They were just manufactured later and into the 20th century. You can lift most table top models very easily.
You can disassemble a standing flywheel platen and get it through a tight place (says me who has one in my home basement.) It’s not ideal though, and very heavy. I used a refrigerator dolley to get it down the steps. Not fun, but it’s there and I never can move again. 🙂
Take a look at Letterpress Commons for some good advice too, especially about impression depth. Be careful to not smash your vintage type if you are going for the deep deboss. Use polymer! http://letterpresscommons.com/impression/
I totally agree with Jen! Sometimes you find the most beautiful wood underneath all those coats of grime and paint. We have several that have turned out to be cherry and look gorgeous when refinished. I think a cohesive natural look (rather than industrial avocado green!) has better value anyway if you were to resell.
Do you have metal trucks or rubber expansion trucks? If metal, you might be right and they may not be the right size-or-do they have a flat, worn spot? I worry if you put too much tape on the bearer rails because then you are elevating the entire roller action which will cause inking problems on the letterpress form.