Setting the gamerule sendCommandFeedback to false makes every other command block say "Not loaded" which completely defeats the purpose of the mod. Doing this also makes the menu laggy.

Command Block IDE uses the /data get block command, and the feedback from it, to load command block contents. As you noticed, turning off command feedback prevents this from working.

I may add alternative methods of loading command blocks in the future to fix this, but, at least on vanilla servers, they likely will not work as well as /data get.