I am not sure what to suggest for you. I'll tell you what I have in my somewhat different setup on my 5870 card.
1. Mini-displayport to 27" apple display.
2. Mini-displayport to VGA adapter (qualifies as active) to a 17" VGA display.
3. DVI and optical to the following converter (also qualifies as active)
DVI & S/PDIF Digital Coax/Optical Toslink Audio to HDMI® Converter
So I have the requirements on the card using two active adapters.
Your setup is a problem. I don't know what to suggest. You could use the same TV setup I have to get one of the two active adapter requirements. That leaves the remaining mini-displayport connection. I don't know what to suggest there. You could see if you could "get away with" just plugging it in and see what happens. Maybe you will get lucky.
If you keep the TV connected to the mini-displayport there is no mini-displayport-to-HDMI active adapter for that I am aware of. None are even listed in the "AMD Eyefinity Validated Dongles". You would also then need an active adapter for the DVI to mini-displayport connection. For the 27" screen the only adapter/converter that I know of for that is,
Atlona (Dual Link) DVI to Mini DisplayPort Converter
Not cheap. And that still leaves figuring out how to connect the TV with an active adapter.
I think I've given you all the information I can on this. You will have to decide what to try to do. When I was first investigating this I spent a lot of time google searching for "X-to-Y adapters" and "X-to-Y active adaptrs" for various X's and Y's to see what I could turn up. You may end up doing the same.