Tom, I'm surprised that your getting those results. I have tried the EFA quivers on a wide variety of bow with no visible change in where the arrow impacts. Bows that I used range from a lightweight Saluki horsebow, Martin longbow, Hummingbird (Alpha Male)longbow, Hummingbird recurve and currently a Beeler longbow.
To further test this I put our "Totem" quiver on the Beeler longbow which is what I took to Denton Hill this year. To really test it I used an extension which put the mounting brackets about two inches past the fadeouts. I had the good fortune to win the "Eagle Eye" competition there with this setup with very little shooting beforehand. Last night and on Tuesday night I shot this bow with the guys without the quiver with the same good results. I had taken the quiver off to put on another bow and just hadn't bothered to put it back on.
As A. L. Adcock said "Yes, they change the tuning, no matter what type", it will change the tune. However, does it change it enough that you can see or measure it. We work diligently to keep our product lightweight so that it won't alter the shot. That's why we started making these ultralight 3 and 4 arrow quivers, so that you could put it on the bow or take it off with no noticeable consequence.
I suspect that there are a lot of factors that are involved here. How you grip your bow (tight or loose), the type and weight of your bow, the weight of the arrows that you use, shooting style, as well as the quiver itself and how and where it mounts to the bow, all might play a part.
We do guarantee that you won't see any difference in how your bow shoots (except maybe quieter). If you feel that it does, you may call to make arrangements for returning the quiver for refund.