American-sized (i.e., big) gongfu teaware?

Two steeps from a 150ml pot like this –
http://www.chawangshop.com/index.php/tea-hardware/other-teapots/white-porcelain-teapot-150ml.html

or three steeps from a 100ml pot like this –
http://www.chawangshop.com/index.php/tea-hardware/other-teapots/bone-porcelain-teapot-rong-tian.html

poured into a large mug, should satisfy your requirements in a cheap and effective manner.

Edit: I missed that you mentioned that you don’t particularly like pots, maybe you could still give them a try, they are not particularly hard to maintain or clean and far more easier to use if you are not dextrous.