First of all, there's a lot of misinformation all over here so relax...
You do NOT need a magic band to use FP+ inside the parks. The Fastpasses basically work exactly the same way, except you go to a Kiosk, touch your magic band (or your RFID ticket for Annual Passholders and/or those staying offsite) and make your fastpass selections. I tested this last week and EVERY ATTRACTION had day-of fastpasses available. Times were somewhat more limited than what those of us who had pre-selected online had available a month earlier...this will be tighter during Christmas week of course.
What has changed is that with parkhoppers, you can ONLY use your fastpasses in one park per day -- you can still hop as much as you want. Simply do the headliners in your first park first without fastpasses (except for holiday peak weeks, you can do the headliners in 90 minutes in all the parks at park opening) and save your fastpass+ reservations for the second (or third) park that you visit.
Last week, by the way, all the paper fastpasses were available -- this week they have eliminated those at DAK -- that is still in testing and most likely will NOT be the case at the other parks until after the holidays. You should be able to get all the paper fastpasses you want during your Dec 21-29 trip in all parks except DAK.
As to times being posted, the Disney sight has NEVER had accurate times -- they post what the ride/attractions actually shows which doesn't match reality re: stacked times, etc. If you want accurate times, get the Lines app from TouringPlans.com...