13Kw genny supplying a 60 amp breaker? Personally, I think that's about as close as it gets - though the reasoning applied in that other thread would ask you to reduce that panel feed to 50 amps. Naturally, that also could lead to a discussion of whether to consider the 'surge' rating of the generator as well.
I think it's clear we're well beyond the scope of proper code concerns, and into design issues. Time for the 702 code panel to back off, IMO.
As for your maintenance program ... generator makers have been adamant about the need for the generator to operate 'under load,' which they define as about 80% capacity. This is due to concerns over 'wet stacking.' I'm not entirely clear on that issue; I take their word for it. The reccommended exercising is for a somewhat longer period as well; I think they want everything to become fully warmed up.
To be fair, I haven't installed anything that was smaller than 50kw, and it's possible that these issues are not as critical in smaller units. The units I've installed have typically been set up to run for an hour, under load, once a month.