They do indeed come with a tray. I bought that same model with the copper-style lid and it came complete. Those are good skillets and i love the cooking surface WITHOUT a non-stick coating.
On this Hoover skillet??
http://cgi.ebay.com/Vintage-Hoover-Electric-Skillet-Fry-Pan-Vacuum-Cleaner-/310272067546?pt=Small_Kitchen_Appliances_US&hash=item483da807da
My vote is for less detergent and very little softener. If its towels only (no washcloths) and hot water, takes very little detergent. IMO powder seems to give a harsher towel than liquid.
Also, use some kind of rust treatment on the feet to loosen them up. The machine should be nearly impossible to "shimmy" into level-ness unless your machines feet or the floor itself is not quite right.
Mine is a very late version of the 913, thats why mine has the 918 coloring. These are only hard to push on loose or soft-padded carpet.
Seen this link? And a pic you man have seen...
http://www.vacuumland.org/TD/ARCHIVE/VINTAGE/2007/1630x10.htm
You can work around it. A good powder like Tide or Foca is best. Load lightly so the powder gets distributed quickly. Use a longer agitation, or add a soak period.