Maybe, but maybe not; or, It all depends
As with most questions about private foundations, the answer to your question depends on the details about: a) your specific situation; and, b) how exactly the IRS has interpreted the relevant tax code. To figure out what options you have, and which will work best for you, you need to talk to a tax attorney who has worked with foundations.
That said, it seems to me that the natural way to accomplish your goal is by treating your work as a “direct charitable activity” of the foundation. “Direct charitable activities” are, as the name suggests, charitable activities that the foundation does itself, rather than paying someone else to do. The money used to pay for “direct charitable activities” does count against the distribution requirement.
You really need to talk to a knowledgeable lawyer. In the meantime, you might find this survey of the relevant law, or this survey of what foundations are actually doing, useful.
Talk to an attorney about “direct charitable activities”!