You guys have only found half of what you need to get your hay to dry faster here in the Northeast. Tedders are great, and yes they are a tremendous help, but if you really want to help speed things along, you also need a rotary rake.
Y'all are simply happy with the tedder results. Get a hold of a rotary rake and you will be completely beside your self. This gets to be even more critical as the days are getting shorter and the ground is getting wetter.
Tedders spread out the hay nicely, and this is fine for drying when the ground is fairly dry, or at least not soaking wet. After the hay has been teddered and dried for a good day this time of year, then you want the rotary rake to stand the stuff up off the ground and really let the air get to it. Also, when you rake an existing wind row, you will always have what was on the bottom of the windrow on the side of the new on. No more just flipping it over right back onto the wet hay on the bottom. How much the windrow fluffs when you rake it is as a great indicator as to how dry the stuff has become. Get enough experience with one and you can tell how dry the hay is right off the bat. I have only ever had one regret about the rotary rake I bought 6 years ago, and that is I did not do it sooner. Point blank, I WILL NEVER EVER EVER use a roll bar rake again as long as I live and do hay. (Wheel rakes are a complete joke up in this area. They may be okay down south, or where you have really flat ground but that is not here. They pick up all kinds of green stuff in your dry hay.)
Rotary rakes will really allow you to save much rained on hay. The problem in rain wetted hay is that the bacteria and micro organisms are trying to reclaim the hay to the soil. Tedders spread the hay out and give max exposure to the bacteria. Now do not get me wrong here, you need the tedder to start to get the excess water off the hay, but once you start to get that smell in the air that they hay is starting to go south, this is when you need the rotary rake to stand as much of the hay as possible up off the ground and away from the bacteria.
Good tedders are great, but until you get the rotary rake you still are not doing the best you can for your hay.