Dissipating Heat from Tiny Components
Although I'm a little surprised as you at the lack of a pad, a quick back-of-the-napkin calculation makes me think you may be OK as-is.  

The datasheet shows you stay above 90% efficiency through the entire operating range.  And with 5V@2.5A, you're dealing with 12.5W...so you may dissipate, at worst, 1.25W.  Multiply that by your 28C/W Junction to Ambient, and you come up with 35 degrees C.  Subtract from your 125C maximum junction temperature, and you get 90C ambient. So as long as the air around the chip is less than 90C, you should be OK.

By the way, if you can afford the cost, you might be able to save yourself the trouble of manually tinning the traces by increasing the thickness of the copper on your outer layers.  I can't tell at a glance what the copper thickness of that board is, but if you specify "2 ounce" copper for outer layers, it will result in thicker traces and a larger cross section to carry current.  Default is usually 1/2 oz or 1 oz.