Swept Profile Boolean Subtract

Separate configured partstudios by type seems the way to go in my opinion.

Create a base model of each Type: Drawer, Cabinet Frame, Sink, etc.
Configure some length width heights for each (or whatever is relevant).

Then derive those into a partstudio with superderive (which can snap your parts into position in the same command)
From there make your fine tune edits (face offsets, special cut-outs, handle locations, etc)
Or do the in-context method you currently are. Either way will work, but in-context requires more management to update the contexts.
If you don't change the context too often, then in-context would be the way to go.

Each finishing partstudio that your fine tuning in should hold one cabinet frame, and as many drawers or accessories that attach to it, like a sub group of adjacent parts.

Like you may have one for the island, one for the sink counter, one for the overhead cabinets, etc.

so you should only have a dozen part studios, not hundreds.

Worth an experimental attempt at least