I have experience with 2 types of rust proofing methods I'd recomend, 1 I wouldn't, but they all work and the 3rd may help with sound proofing.
1) POR 15 - This consists of a surface wash solution and black paint type coating. It is NOT good if the parts will be exposed to light, but floor boards obviously won't be. It is easy to apply and lasts for years. I had some very rusted surfaces that I coated about 10 years ago and they still don't show signs of rust...and I'm on the east coast. PA
2) Cold galvanizing paint - "Grainger" sells this stuff which has a very high zinc content and it works great too. Plus, it is not affected by sunlight. The brush on kind works better than the spray on kind. I've used this stuff on metals that are burried, so I can't say what happened, but it was approved for use by Civil Engineers for the application.
3) Last one that may help with both your goals is also the worst option if you need to go back and re-do the floors or anything else. It's the type of fix that sounds good now, but later you (or the next owner) will curse up a storm because he has to deal with it. Also, sound proofing a 35 year old convertable is....probably only semi-sucessful. You could try a Pickup truck liquid bed liner. This stuff seals out oxygen and water and puts a thick plastic coating on whatever you paint, so it should quiet things down. I used it in my jeep floor, but that is an off road vehicle that is all beaten to hell.