um, do you have same pickups (I know you said yes, but are they the same for certian? and all mounted Exactly the same way)? same pots? same capacitors, same everything electronics?
Do ALL your other guitars have the same size trem route as the Ibanez?
Basically, what I'm saying is this, the Edge, if anything will create a warmer thicker sound due to it's casting nature. It is a heavier trem, it will transmit better than any of the plate steel trems like the OFR's. The edge points yes are less contact, but not so much that it's a huge difference.
Remember, MOST Ibanez guitars are Basswood, MOST Fender's, G&L's are Poplar, Alder, Mahogany, pretty much everything BUT basswood.
Very few Ibanez's are Alder, some are mahogany, but MOST are Basswood.
Also, the Ibanez body shape is substantially different than me\ost, the horns are thinner, cut aways scooped further, lots of things.
What I'm saying is, it is NOT apples to apples at all, it's apples to oranges. I would go out on a limb and say that your Fenders and whatnot sounding thicker, or bassier has more to do with the electronics, and body woods, even the finishing system used between manufacturers can create different tones.
What pickups ARE you using? (why do you have what sounds like a lot of guitars with ALL the same pickups anyway?) you have to remember, the difference between a 250K pot, and a 500K pot, is quite a bit, same with capacitors, resistance in wire length on the pickups, it's all small stuff, but it all adds up.
And bottom line is, sometimes you just have to accept a little down in a bigger up. The Edge is the most stable trem you will ever find, Personally, I'm willing to lose a little bit if that is the case in tone for the stability.