I just recently faced a very similar situation and replaced a well worn Sachs 6 speed (13-26) with a new Sunrace 14-28 and a KMC chain on a Cyclone 7000 setup. I haven't had any hiccups in indexing so far in about 50-60 miles of riding. It shifts really well. Sunrace 6 speed can also be found in 14-24.

One caution I would add is that this new freewheel is not nearly as smooth as the others from Sunrace I have put miles on. I may swap it out for a Shimano 14-28. It is the first time I have had an issue with a Sunrace freewheel. It's funny because I just did 20+ miles on another bike with a 14-24 6 speed Sunrace and it is completely fine.
My setup: