I feel your pain OP. We were there last week as well and the parks were very crowded. Our rope drop plan is to head to "fastpass worthy" rides, but try to avoid the rides were the majority of people are going. We had two MK days last week (Tue and Fri). Tuesday was very crowded and since it was an EMM morning there we decided to rope drop Adventureland and get Jungle Cruise, Pirates, then Splash before our first Fastpass at Big Thunder Mountain. I figured the EMM crowd would move to Tomorrowland after finishing up with Fanstasyland. Our other fastpasses were Mine Train and Space Mountain.
Friday was less crowded and we rope-dropped Space Mountain and were able to ride it a few times before the line got to over 20 minutes long.
Even though the parks were very crowded I think the "refresh" strategy for fastpasses after the first three worked very well at Magic Kingdom. After lunch when wait times were peaking everywhere we would just choose what ever had the next closest time and used them for rides like Small World, Tea Cups, Under the Sea (rides that are not worth waiting a long time to ride), modifying them if necessary to keep moving up the times. We waited to late afternoon to look for fastpasses for more popular rides like Haunted Mansion and Buzz because the times were already several hours out, but could get those if you kept modifying. On our Friday MK day we were pleasantly surprised to see a Mine Train fastpass show up for 8-9pm (for 5 people no less).
I will say that during our week we saw so many rides close for issues each day which caused already long wait times go up. Test Track was closed for 8 hours on Presidents Day and closed again when we rope dropped the EMH hour on Thursday. I very nicely explained to Guest Relations that we were not having any luck with Test Track and they added a fastpass for us which was very nice. The ride closures definitely made plans change, but sometimes it actually worked out better where our fastpasses were replaced with the any experience ones. Living with the Land and Frozen were also closed for extended periods on Presidents Day. Big Thunder Mountain was closed for extended periods on Wednesday. A Bug's Life stopped working when we where waiting on Saturday. Primeval Whirl broke down when we had a fastpass (we used the replacement for Everest). Buzz broke down when we had a fast pass (we used the replacement for Space Mountain). Tower of Terror broke down when we were in line - we just had to move to a different elevator. Star Tours broke down while we were in line. There were just so many issues which seemed to make waits even longer during the week.