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Nothing will permanently stick to it.
This leaves the glue gun approach. I've seen some good results on forums of drilling a support hole into each tread area, masking it off and building up the area with the glue from the support hole. Not sure how good it will be or, if they'll be any longevity, but it could be worth a go.
@bluebikerider I don't think Quoc's have a replaceable sole either, but they're far more reasonable in price. The only other office friendly / leather cycling shoes I've seen with replaceable sole/tread bits are the Giro Republic's. However, these wear really quickly. Expect to buy lots of replacements if you walk lots.
Since they're leather, I thought this might go here. I've a pair of Maressi shoes and need to sort out the sole. Anybody got any ideas of how to build it up as there isn't much cleat clearance anymore?
I've seen the glue gun approach with masking off the tread areas and building it up, and I've seen grinding everything off and replacing it all with a Vibram sole. Anything else I could try?