If you need a new ESA and can't get an original one I'd call CDI electronics in Alabama and ask them if the one they sell still uses the overstroke switch. When I replaced mine a few years ago, the one they were selling still used it. So when I installed the new switches and CDI ESA, it was set up as original and worked the same way. Try Crowley Marine in Colorado if you want an original that is updated, if the one CDI sells is not.
When I had the problem with mine, it appeared that the shift assist switch was sticking on, but the overstroke switch was not cancelling it. If you look closely at the switches, you can see that the button part wears over time, these switches that I replaced about 3 years ago were original.
If you want to test yours, you can do it as Bruce says, but try to do it on a day when there is no one around so you can shut off the engine to get it out of gear, since you will probably have to do that in order to not put too much strain on the shift linkage.
After I replaced the switches and ESA (mine failed right after replacing the switches!) mine was back to smooth shifting.
Try to get the idle as low as you can, ie 550 or so in fwd gear in the water.
Keep in mind there are other things that will cause an engine to not perform well after shifting in gear on the water. With the ESA sticking you can tell because as soon as it happens, the idle will be abnormally low.
However, a corroded anti siphon valve will restrict fuel flow to the point where it will cause the boat to not accelerate in gear. It will start ok and idle fine and you can rev it up in gear, but put in gear and put a load on it, it will fall on its face even if there is nothing else wrong. Try what Bruce said before buying parts, and report back. My boat had the anti siphon valve problem back when we first got it.