Where is your most critical access from? Front? Are you putting plywood on top?
The reason I ask is if you put plywood on the top you can eliminate all of the bracing on the front. The plywood will act as a diaphragm to transfer any rotation/sidesway of the stand into the three other walls. If these walls are braced you are good to go.
As a quick calc, I checked the max earthquake force for northern Indiana. I believe it's around 1200 lbs of horizontal force. With 6 legs (and no braces) this is 200 lbs per leg. How tall is the stand? Two feet-ish? From a strength standpoint, I don't think you need gussets for this. From a stiffness standpoint (and piece of mind

), some bracing may be a good idea.
If I were you, and I only needed access from the front, I would put a 1.5"x1.5" diagonal tube running from joint to joint (top left to bottom right, etc) on each of the three sides (only one brace at the back). This would make it ridiculously stiff (provided you have the ply on top and still keep the front wide open). I also think this would be cheaper and easier than messing with a bunch of gussets. Using a brace tube that is slightly smaller than the frame tubes will allow for some easier welding, too.
To stiffen the top rail, adding a seconds piece of tube underneath it would allow you to keep the extra legs out. You would need to weld the two tubes together at regular intervals to keep them acting as a single piece. I think a 2" long weld at 6" on center on each side of the tube would do the trick.
Let me know if can help with anything else.