On the NOZOMI train from Kyoto to Hiroshima and back
 

Is it worth the extra 3,590 yen to go from a reserved seat to a green (first class) seat? Trip is 100 minutes. We will be going at 8 am and returning at 7 pm or later.

Not worth it, in my opinion. A reserved seat in regular class is quite comfortable.
I think the price difference that you're quoting is per person, each way. (Correct me if I'm wrong). So, assuming that "we" means two of you, you save 14,000 yen in regular class. That will pay for a nice dinner.

Unless it's a busy holiday period or something, I agree with jib71 but ultimately it's your decision to make. I took the green car once from Tokyo to Shin-Osaka and it was nothing special. You can find various reviews/trip reports in which the author rides in the green car if you are truly curious and need help making up your mind.

I've found this as the one of best resources between train classes. The website as a whole is a very good resource on rail travel in Japan.

We will be traveling on Sports Day, a national holiday following a weekend. Predictions are for heavy crowds. I think we will split the baby so to speak and do Green just on the trip back to Kyoto. By then we will have not only traveled to Hiroshima, but spent some 8 hours touring it. It may be worth the $32 each then.

You can get guaranteed (reserved) seats in the regular car. Since it's a reserved seat car, everyone will be in a seat and no one will be standing in the aisle. So the potentially heavy crowd will have no effect.

I personally think it's worth it but there's no real right or wrong answer. Typically, green cars are much less crowded and also a lot quieter. Being that they're the closest thing on that train to first class, most people seem to treat them as "quiet cars" as well. I have actually seen Japanese people shush westerners (in their own party) who were being too loud in the green car on that very route.

Reserved cars are usually fine but especially if they're full, you've got just as much chance of sitting near screaming babies, drunk groups of adults, or rowdy teenagers as anywhere else. It's still possible in a green car but just a lot less likely. Also, reserved cars are 2+3 whereas green cars are 2+2, so you do have a little more room. (There is plenty of legroom in the regular N700 cars, but you get more width in the green car.)

Green cars also get the snack/drink cart more often than the reserved cars, and also first when they restock. Often they will be out of a lot of stuff by the time they get to you in a reserved car if the train is full. Might not matter to you but I always like to get something from the attendant.

>> Also, reserved cars are 2+3 whereas green cars are 2+2,

Ordinary Class reserved cars are 2+2 on the Mizuho / Sakura (which runs from Shin-Osaka ) , while non-reserved are 2+3.

Be aware the green car seats are only 1/2 a carriage on Sakura trains, and since such a small part of the train, they do sell out at times