I know, i LOVE my cups of tea
I simply switched to a brand of tea which has minimal tannins in it. There is one brand which is grown here and sold in the supermarket as well as over the net. It's called "Madura Tea" and it only has 2.8% tannins and one of my previous doctors actually got me onto it.
As for coffee, i found a couple of different ones in the supermarket which are not made from coffee beans, but from barley and some other natural things and therefore contain zero caffeine. It wont taste exactly like a true coffee but does the job. I most love my coffee first thing in the morning with breakfast so that's when i have a normal coffee (i love Moccona) and then i have my iron supplements at either morning tea time at work or with lunch.
Despite cutting down on the caffeine it's done nothing for my ferritin levels. I ended up finding out that i had a digestive issue which was linked to my thyroid issues. So i guess i can go back to not worrying about tannins etc but i'm used to it now.
So take a look at what is out there as there are some great products which can fill the void. The almost tannin free teas taste exactly like the 100% tannin teas. It's only the coffee's which taste different, but then again you can have your coffee but well away from main meals or iron supplements.