The Renault internal selector/synchro system is a bit baulky. After the synchro does its job, if anything holds up the actual shift, it will grind. It’s more common when cold as the colder, thicker oil holds things up. Your main issue is a worn synchro BUT it has been exacerbated by your “tightening” up the shift linkage. This slows the action of the shifter and causes enough of a “delay” to cause grinding. The real fix is to pull the box and replace the synchro/gear. In this case, you can go back and find any areas where you may have tightened your loose linkage too much and induced drag, and loosen them a tad.
A synthetic gearbox lube helps a good deal as well as it doesn’t get as thick when cold. Redline MT80 (off the top of my head) is a good choice. I’ll double check on that.