OK, you're right, the problem is they have a different bootloader on the ACEduino Mega (ATmegaBOOT_168_mega2560 vs stk500boot_v2_mega2560) that runs at a different baud rate (57600 vs 115200). So I think you should be able to just use the current IDE to burn bootloader to your board as an Arduino Mega 2560 and use it as an Arduino Mega from there on. The ACEduino is actually 4 kB smaller than the Arduino bootloader but 4 kB isn't really a huge deal when you have 256 kB to work with. There is actually a really good 3rd party hardware package for the ATmega2560 (MegaCore) that has a 1 kB bootloader if you ever are cramped by the bloated stock Arduino bootloader.
PS. I believe that the ACEduino bootloader has the eternal loop after watchdog reset bug.
It's really sad that a company that manufactures and sells Arduino board derivatives is so completely clueless about how the hardware definition system works that they think they have to ship an entire copy of the Arduino IDE and even worse that they haven't bothered to update that IDE version in so many years. It shows they really don't care about the users of their products or about the Arduino community in general. I would avoid buying from Alexan in the future if at all possible.