Your HI's plan sounds pretty good. Just want to add/clarify a couple of things.
Use 6 mil thick plastic sheeting. I can be found in the Paint Aisle in places like Home Depot or Lowe's. (Ask around if you can't find it. Just be sure it's 6 mil in thickness ...)
Keep it out of the sun. UV rays will 'break down' the plastic.
I'm not sure what the purpose of the insulation on the walls is. I'd ctc him on that. I'd do that if it was a heated crawlspace. If it was heated, the warm air in the crawl would actually draw in moisture and cold 'through' the wall adding to your problem.
Plugging up the vents is dependent on where you live. In my area (SE PA), we don't cover the unheated crawl vent covers. We DO insulate the floor above the crawl as well as the pipes and ductwork because it is kinda 'outside'. Just to be safe, ask around. Even try to ctc a Municipal Inspector for his $.02. (If they won't help, ask them for some leads ...)
I wouldn't insulate the floor at all. The gravel is meant to simply keep the plastic from curling or lifting; it doesn't add, or take away, from anything that has to do with moisture in the crawl.
ANd lastly, personally, I wouldn't tack plastic up onto the bottom side of the joists. It's been known that when the air that's 'trapped' between the plastic and the bottom of the floor (above the crawl) gets warm WHERE the air in the crawl, itself, is cool, condensation will form on the WRONG side of the plastic. This could lead to mold/mildew/dry-rot. Depending on your crawl's set up with regard to the rest of the house, and where you live in the 'world', it may be counter-productive (IMO). Generally speaking, the vapor barrier is to be installed on the WARM side; not the cold side. WHen it comes to a floor over a crawl, the vapor barrier is installed on TOP of the joists (the warm side.)