Where should I run the plumbing, under or through the base cabinets?
I'll always vote for accessible plumbing, with or without splices.

If, in the future, something goes wrong (murphy's law!), then (1) you'll see it before it becomes a huge problem and (2) you'll save a fortune not ripping your cabinets apart.

If you have (or can engineer) easily removable toe kicks, then that would meet my standard for accessible.