IMHO, Leave the Burton bindings with the Burton board, get F2 bindings with your new EC board later....
Bindings flex for EC is not that much important, the guy that got me into EC (witch is now a very good friend, and local rep for Swoard Snowboards) rides with F2 Titanium Intec witch is supposed to be "too stiff for EC", doesn't seem to limit his EC ability! I changed from F2 Titanium Intec to Carve Intec RS on my EC board because I needed a second pair of binding for my new Coiler Nirvana and wanted to save money on new binding. I found the F2 RS softer and more forgiving, but it's with practice and someone else helping me with my technique that I got better.
My 2 cents about important stuff for good EC:
1st - Technique
2nd - ... technique...
3rd - Boots... (confy with enough flex)
3rd and a half - EC Board
4th - bindings