I gave up with 6700 series after a few STI failures, Shimano was new to the underbar cable routing, and this first gen was pretty bad, my failures sound similar to yours, and at a similar distance.

I went to 11 speed (6800) after 6700, being as you want a triple, this isn't an option. If I was in your position, and wanted to keep the triple (once you throw in the 11 speed hub/new wheel, it's getting an expensive repair), would be looking at Tiaga (4703) knowing that the RD would need to be replaced as well (If you have done 16k on your current one, it has had an ok service life.

Tiagra (4700 series) also has the advantage of the better ergonomics of the 6800 series (although still a bit behind the latest R8000) and as there was a minor re-fresh this year, 4700 doesn't seem to have a replacement in the works just yet to hold off for.

If you really don't want a 11t on the cassette, forget 11 speed as an option, as almost all 11-speed cassettes are 11-xx, trying to find a 12-xx is hard to impossible (I've failed to find one as yet)