Assuming I'm not missing something, which is a possibility, you would have to cast spell enhancer on the round immediately before or the same round as you cast the spell you want it to effect dye to the 1 round duration. Now, aiming you wanted to combine it with elder giant magic, things either get a bit complicated due to the single round duration, or really simple. This is because the verbiage of spell enhancer specifically states functioning on the next spell you "cast" and only having a one round duration. Technically using EGM means that the spell wouldn't be cast when spell enhancer expires but still in the process of casting
Now, if I were Dming, I'd probably make a house rule and allow it to function. I can't really think of anything that the extra +2 Cl would break that I allow anyways.