Puts are all based on the ex-dividend price... so that would be Spot-Dividend... That's probably why you think they have a huge extrinsic value, which they don't.
Extrinsic value will not increase.. because why would it? There is nothing to be gained here.
Re-analyze with spot - dividend and it will be more clear to you.
As for ITM calls, some are based on the current Spot, and those will/should be exercised before dividend. ATM and OTM calls are all based on Spot-Dividend as well, like the puts... maybe with a little bit of extra premium because of the exercise option you have before dividend.
Don't exercise your puts before dividend!!!
Uhm, IB says dividend SPY is 1.141 USD at JUN 16 '17... but that's probably not correct... I would say SPY has the ex-date at/around the same dates every time, probably quite stable dividends, since they reflect the dividends from the S&P500.