Hmm, tough one!
I tried to find more information beyond what you found out, maybe even a newer BIOS, but came up empty. Whether or not your E4400 will work is really hard to say.
What I can tell you is: it's worth a try. It won't be damaged even if the BIOS doesn't accept it; worst case you'll simply have to find an E4300 or go back to your current processor.
The other option - flashing your BIOS with one provided by ECS for the "M" (not "HM") motherboard - similarly may or may not work. But if it doesn't then you'll have bricked your system and be unable to ever get it working again unless you have some built-in BIOS recovery option.
A third option would be having an experienced person modify your existing BIOS and try to add support for CPUs beyond the E4300. I'm not sure if this is even possible, but I know of a forum where you can submit a request to have such a mod done. Of course, again this is completely at your own risk as you'll have to flash the modified BIOS on good faith that it'll work (they can't test it for you).
http://bios-mods.com/
Out of curiosity, which CPU do you currently have installed?