I have gotten a varied number of opinions on comparisons between the Sunking and different versions of the Klon. Some report minor differences and at least a couple have said it was dead on. There are, of course, differences in terms of being able to attain the exact sounds, namely in the diodes and the special dual-ganged gain pot used in the stock unit. But, I've never heard that anyone thought there was too much bass. The gain thing puzzles me a little, too, based on my own experience.
If you've got the Klon handy, I'd be interested to know what resistance you measure on the two outside lugs of the two ganged pots, and how they compare to your DIY build.
Certainly, your DIY build could be tailored to reduce some bass, if that's what you are after. If you feel there is too much bass on the clean settings, try reducing C5 to 330n or even 220n. On the dirt side, you could reduce C7 to 68n or 47n.
To get more distortion, I would try using 1n34a diodes, which will have a slightly smaller forward voltage. You could also try a 250kB dual gang pot for the gain.
I think these mods might bring it closer to what you are hearing with your actual unit. Also, for best comparison, I would test them independently (if you already haven't). If they are arranged in series and you are toggling between them, it's possible the bypass (buffered) mode could be altering the tone in small ways as opposed to being plugged straight into the amp.