Supports wont touch the model

[DaynoART 0]

I'm reasonably new to 3D printing, and have been using Cura as a slicer the whole time. It has worked beautifully up until recently. Upon slicing my files, those supports which are immediately above the raft/print bed will be appropriately rooted and stable, but the supports which would need to be rooted directly on the part are instead floating. I significantly altered print settings (support z-distance=0, Z overrides XY priority) and managed to get the support structure and the part into contact, but so barely that the supports inevitably fall off while being printed. Similarly, the underside contact points with the part are barely making contact. By using tree supports, I've partially sidestepped the bottom-anchoring problem by guiding roots onto the print bed again, but even tree supports aren't making contact properly with the part. Figuring that I must have toggled something, I reverted to install presets, but it didn't change anything. I deleted Cura and downloaded 4.7 which conveniently was recently released. Still, same problem. I'm running out of ideas, help please! Thank you

 

I'm using a Creality CR-10

 

IN SHORT: My support structure is anchoring well to the build plate/raft, but not so to the part I am printing. 

Edited September 3, 2020 by DaynoART
clarification