Pick up the diaphragm kit before you open it up. To remove the heads & not change the diaphragms would be a real waste of time. They're leaking as it is. When you get it open, you'll almost surely find that they've aged & cracked. Change them now.
Depending on the number of hours you guys log on a sprayer every year, I'd recommend changing the diaphragms every year (or every other at minimum). These buggers are very reliable as long as they are supple. They will age & stiffen even if they're not being used. The $50.00 kit is nothing compared to the cost of tying up the sprayer for a whole day. One customer lost to weeds in April or May more than exceeds the cost of changing marginally worn diaphragms.
When storing a sprayer for more than a couple weeks, it's a good idea to run a Nutrasol or Lescosol like tank cleaner through it. While most commonly used to neutrelize herbicides, these cleaners also counteract the harsh effects some chemicals have on the wetted parts of a pumping system. EC's are worse than flowables & wettables but any chemical can cause degradation. The old insecticide Triumph used to eat Viton diaphragms over a period of about 4 or 5 days even if the unit had been flushed with water after spraying.
The washers sound correct. The turned edge that is exposed by the cupping should face outward or toward the head. Check that freezing didn't cause damage to the heads while it's apart too. When reinstalling the new diaphragms, make sure to clean all the parts carefully. Dirt caught between the viton & the vinyl coated aluminum will at least cause leakage & at worst, warpage of the head. Pretty uncommon, but I saw it once.