Logically speaking, if a person only had 3 oz. hops, they would likely space out the additions at various time slots, e.g. 60/30/20/15/10/5/0/Dryhop. I'm not saying they should add a small amount of hops at each slot, but the point is when you do something like this, 3 oz. isn't much for your basic American ale. However, if you blast it with a hefty bittering charge and then use the leftovers for the dryhop, chances are you will not have a very good beer.
I did:
.5oz CTZ @60min, 13.9%AA, 21.3 IBU
.5oz CTZ @30min, 13.9%AA, 14.9 IBU
.5oz CTZ @5min, 13.9%AA, 3.9 IBU
.5oz CTZ Dry Hop
.5oz Centennial Dry Hop
40.1 IBU is at the TOP end of bitterness according to BJCP guidelines for American Amber and my 2.5oz of hops were spread out. Again, 3oz of higher alpha hops is more than enough for the style. Even 3oz of lower AA hops like cascade is enough if you aren't trying to make a hop bomb out of an American Amber.
An amber i did last year with Cascade:
1oz Cascade FWH, 7.2%AA, 21.9IBU
.5oz Cascade @30min, 7.2AA, 7.7IBU
.5oz Cascade @15min, 7.2AA, 4.9IBU
.5oz Cascade @5min, 7.2AA, 7.0IBU
.5oz Cascade @flameout
.5oz Cascade Dry Hop
That's 3.5oz (and could have done without the flameout or dry hop) in a 5.5G batch, again, well spread out, 36.5IBU, still in the upper half of the bitterness for the style.
I'm lost on how you figure 3oz is "a very low amount" for 5G of Amber.