Time to expiry is pretty damn hard to properly calculate especially if you are dealing with really short dated options. Would you only care about the business (trading time)? Would you care about the night hours? Anyway, in 99% of cases, it's not the time to expiry that's gonna f*ck you up, it's the dividends and the borrow which are going to effect everything. Not a single retail option broker that I've dealt with has bothered with bootstrapping the forwards properly, check it out for yourself. In terms of time to expiry, as long as you are consistent and are not making markets, you will be ok either way.
If you can get the real time quotes during the day, you should see the closing prices when the market is closed.