Sounds like you need to dial in some vertical lift to lift the nozzle out of the way whilst moving......the setting is in the Ooze Control section in the Extruder tab. You'll need retraction on for this.
What you're suggesting is happening is just the nozzle skimming the previous layer during movement...and as the model gets higher, the effect looks as if the nozzle is skimming closer...but its not. Its the printed part tending to flex easier the higher it gets.
I'm not sure that's it. It moves the print around while it's printing the next layer. While there's a good size gap when the first few layers are printed, that gap shrinks to the point that it starts moving the print around while it's printing.
I did find a spot under Tools > Firmware Configuration where you can set the Steps per mm for the axis. I've tried changing it, but the setting doesn't stick.
Printer is a FlashForge Creator Dual
Printing Taulman 618 Nylon
The settings won't stick if you have the "update firmware configuration" enabled in your profiles because that is telling the software to override those settings any time you use that profile. So you can either disable that option on the G-Code tab, or just make the changes in the Tools > Firmware Configuration menu, and Export the new firmware config. Now you can select that new config on the G-Code tab for the "firmware type".
I did finally get a clean print yesterday, and discovered a great way to get Taulman Nylon to stick to the build surface.
Drop a dab of Elmer's Glue and spread it around where the part will be printed. A thin coat is all you need. Add a little more if it's a big part so you've got total coverage under the print.