If the cords bother you that much cut them down to about 12" and install twist lock connectors on the ends and add a twist lock to one extension cord. added bonus is that the plugs never fall out of the extension cord.
That's a bonus, but it gets expensive fast (have you priced twist-lock ends?). Also, now you can only plug your grinder into your special extension cord. A simpler option is to put a non-twist locking connector on the end of the extension cord. Then you just need to buy one special connector, and keep standard plugs on your grinders.
For my part, I've chosen to not cut my grinder's cords. I used to use a velcro strap to keep my cords on a loop hanging from the machine, but re-looping it was just too tedious, so I compromised. I have about 4' of cord coming off the machine, and loop the rest on the plug end with the velcro. When I hang up the grinder, I just need to make two quick loops and hang that plus the pre-velcro'd loop from the side handle. But I still have the full cord if I ever need it, and the loop on the plug end doesn't get in the way of anything for me.
But in my case, I have receptacles with easy reach of everything (plugmold along the bench, and outlets overhead and at eye level along the walls).
I have not had issues with standard plugs falling or being pulled out, and I attribute this to having fairly new and tight gripping outlets. I could always install hospital grade outlets (they are designed with tighter grip on the ground), or use a cord with a locking connector, but never had the need.
As for storage, I hang my grinders upside down from the way they're pictured in the rack. Cord end up, hanging from the cord.
I slit an inch or so of rubber hose, and wrapped that around the cord to protect the cord, and clamped that on with an oetiker clamp. That gets zip-tied to a magnet with a loop, which I hang everything from. In this direction, I can hang three grinders in less space taken up by two in the rack above. I have yet to damage a cord, but I understand that is a risk...