My husband the plumber had these responses when I read him your post:

1) Most tanks now have rubber diaphragms, though not perhaps all natural rubber.  You can get ones where the diaphragms are replaceable so you don't have to throw the whole tank away if something breaks.

2) They make galvanized steel tanks without bladders, but that has higher maintenance costs.  He doesn't think galvanized steel is the best material to use for drinking water (his personal opinion, and suggests checking for others research on this, plus consider the country of origin, made in China is more likely to not be trustworthy). 

3) If you can afford it, put a variable speed pump in, as it requires a much smaller tank and uses less energy. 

I'll just say that I don't understand any of this, I just wrote down what he told me!  I hope there is something helpful in it! 

Thank you, Amy and Beth. 

I posted a question on greenhomeguide.com, but never received a response. I also posted a question to answers.yahoo.com and had one person complain about bad well water and another provided the following: "You should be able to find a glass lined pressure tank (non bladder type). I put an 80 gallon one in my house about 25 years ago and it is still working fine. Make sure that you do not have a plastic well pipe ' cause that will also get plastic into your water :-) The electric wire running to your pump is also under water 'cause the pump is under water."

I could not locate any glass lined pressure tanks that were for small homes. 

In the end, my well guy found Flow Thru F8 by Flexcon Industries. It's a small pressure tank with a special constant pressure device that allows a full flush of water so it is not sitting in a large tank surrounded by plastic. The tank is stainless steel and I think that the diaphragm parts are rubber. I'm going to give them a call tomorrow to double check on everything. I'll report back if I find otherwise. 

http://www.flexconind.com/html…..-thru.html

I'm not exactly sure how it functions, either, but it was the best of all that I researched. I'm very happy with it, but have not yet received my first electric bill. 

I haven't tasted the water because I received the results from one of the water tests and there is coliform in the new well. This is typical mostly because I opted to not have it blasted with bleach when the pump was being installed. I'm now in search of a plastic-free water filter.