Well, the shop manual for the BFP60A is here:
publications.powerequipment.honda.com
Not sure if that would work for you....just tossing it out there.
I like your plan for checking the tank vent.
This does sound like a fuel starvation problem or water in fuel symptom to me but, as you say, it might be something else entirely.
I would definitely "revisit" the fuel water separator work that was done to eliminate that as a possibility. Especially if this started right after.
I've seen cases where those on board water separators with electrical sensors cause problems when they go bad but it's typically more of a warning horn and red lamp thing. I can't recall if they cause a stall like this.
Any chance that you could rig up a fuel pressure gauge and refer to it when the issue occurs?
We have seen issues here with coolant passages getting clogged causing problems that are difficult to diagnose but I'm not sure if I've seen that with the 60hp or not.
I haven't worked on one these so just throwing some ideas your way.
Hopefully Ian...the pro Honda tech that helps folks here...will see this and comment.
Good luck.