RE: Which Tamiya models...
I hear ya there.
I'm certainly hoping Tamiya releases a full function 1/16th Abrams. Seeing as aside from Japan, their largest market is the USA I was surprised they built the Leopard instead.
I think the cheapest you will find is the Sherman you listed. Tower Hobbies has them for relatively cheap when compared to the Ebay price plus shipping rates.
Use a Tower discount code and take another 30 bucks off the price.
OR, not sure if you HAVE to have a Tamiya tank, but the VS tanks for sale on Tower Hobbies all have the infrared battle system. Not sure if it is compatible with Tamiya's firing system though.
AND if that was not enough, many of the Hen Long tanks for sale on Ebay are available in 1/16th scale with infrared or airsoft. Just make sure to get the smoke and sound models. The non smoke models are pretty junky from what I've heard.