I have a D-FA 28-105 that I use on an APS-C body. I ruled out the 18-135 based on reviews that seem to indicate IQ is good but not fantastic, and needs to be stopped down a bit.
The DA 16-85 seems to get better reviews and probably would have been my choice on an APS-C body, but a D-FA 28-105 came up at a price considerably less than it would cost me to buy the DA 16-85, so I decided to give it a go, and I've been very happy with it. Sure, I'd like something a bit wider at the wide end, but 28mm on APS-C is equivalent to 42mm on 35mm, which is still a bit wider than 50mm or 'standard' lens on 35mm, so if you're happy to live without wide angle, then it's a perfectly useable zoom range even on APS-C.
If you're buying new, it might be better to go for the DA 16-85 as it is more or less the APS-C equivalent to the 28-105 on full frame.
Here are some examples with the D-FA 28-105 on the K-70 which is APS-C