We were there those exact dates this past year. I do think that not having the marathon at the end of that week will make a difference. I would say usually the crowds get a little less as the week goes on and you get further from New Years Day, but that wasn't the case with the marathon happening that weekend as well this past year. It was REALLY cold that week and rained more than usual for that time of year, but I think that was just bad luck - I'd pack layers, hats and gloves, and ponchos just in case! The only day that felt overly crowded for us was our Magic Kingdom day (it was the Thursday of that week). I think the weather contributed to that though - the day before (Wednesday) was a really rainy day so I think a bunch of people who planned MK for that day got rained out and decided to go to other parks and then do MK on Thursday - also, Thursday was when the marathon people really started to arrive. Even with that the only time that felt unbearably crowded was right after the Festival of Fantasy parade in the liberty square area...sea of humanity trying to go all different directions! We still had a great time and were still getting additional FP for our group of 5 late into the evening.
My best advice for when it's that crowded - rope drop and ride as much as you can in the morning. Plan your FP+ for late morning, early afternoon and then do shows and things that have no lines (things like Carousel of Progress, Tiki Room, Country Bears, World Showcase, shows at the other parks) in the afternoon/early evening. I don't like taking breaks when it's that crowded because it just feels like it takes longer to get out of the park, back to the resort, and then back into the park - but breaks in the afternoon and then back for shows at night may also work. Also, just plan on being there early to get a spot for things that lots of people want to do (parades, fireworks, etc.).
Have fun!