Ok, rather than blaming everything you need to start performing step by step diagnosis. Brand new cables does not mean that they're installed properly. My guess is that an end ferrule is loose and un-seating during riding, when you shift it gets jammed in a different position changing the cable pull.

First step is to isolate the FD from the cable + shifter.
Disconnect the cable at the FD. Manually pull straight up on the cable with light tension while working the shifter. If the cable moves properly the problem is the FD routing. If the cable doesn't move properly, you've got a kink in the housing or something.

Newer Shimano shifters rarely break. Usually the shifters stop clicking entirely because they're gummed up. Increasing cable tension is a sign of the cable or FD catching on something, meaning that the cause is likely not the shifter.