OP have you tried white noise REALLY loud? I was given this suggestion yesterday, basically to block out outside noises. I'm trying it as I type. I got my DD to settle herself to sleep in her cot which has only ever happened once before (yesterday) and even though she only lasted 30 mins she generally also only catnaps for 40 mins during the day times. It may help with drowning out the construction noise. If you have an iPhone there's good apps avail.