My suggestion: leave the existing 60 amp wire and box, change its
breaker to 40 amps, and use it for the 40 amp load. For the other
load, run a separate, new, 30 amp line with a new box.

Cheers, Wayne

Thanks Wayne. That's what I'm going to ask my electrician to do. I hope
fishing the #10/3 thru the steel conduit with #6 wires in there won't
be a problem. The good news is, the breaker box is also in the kitchen.

As far as some of the other replies go, I have no intention of going
against the code, but as I said in my first post, I got conflicting
answers from licensed electricians, and just wanted to clarify things.