From the compatible processors page under support for that motherboard : http://processormatch.intel.com/CompDB/SearchResult.aspx?Boardname=DH61DL the i7-3770T is not currently (05/05/12) listed (only the i7-3770S as far as i7 CPUs go). If you compare both of these processors though there doesn't appear to be much between them http://ark.intel.com/compare/65525,65524 so if you raise an official tech support ticket with Intel they may be able to tell you if a future BIOS upgrade will give support for this CPU. The lower power usage of the one you want to use may be something to do with it if different voltages are needed.
As far as sucessor motherboards go, keep an eye on Intels website and review sites but if you buy such a product in the early days straight after release you'll surely pay a premium price.
How does one raise an official tech support ticket?
Also to uppgrade bios, one needs an older CPU, which I don't have...
If both the CPU and board were supplied to go together by the same supplier, ask them to look into flashing any possible BIOS upgrade. You raise a ticket (or official tech support case) by going to the Intel Support website for your country and following the options related to desktop motherboard support - here in the UK it gives a phone number to call (at least it did when my old motherboard was still supported). Let us know your country if you try this and are still stuck.
When is the 3770T being released?! It's nowhere to be found!! Also this page Intel® Processors and Boards Compatibility Tool - Search Results Page now lists that any version of the DH61DL now supports 3770S?!?!?!?
What is Intel doing?!