It isn’t clear from your statement why you have to distribute so much of your income.  I assume that you are basing it on the 5% minimum distribution rule, based on the value of the building as an investment property, without regard to the amount of income you actually receive from the rentals.

Assuming it is, one way to avoid the minimum distribution requirement would be to become a “supporting organization” to a friendly local public charity doing something similar in your area.  (See Ready Reference Page:  “Supporting Organizations Qualify as Public Charities”)  As a public charity, you would have no minimum distribution requirement and could build up reserves more quickly. 

You might also qualify as a private operating foundation if the property is somehow used in your charitable program.  If you qualified as a POF, the value of the property would not be the measure of your expenditure requirement, but you wouldn’t qualify as a POF if your primary activity is making charitable grants.  (See Ready Reference Page: “Private Operating Foundations Are Hybrids”) 

If the building is not related to your program, you might just sell it and reinvest the proceeds.  Then you could make your 5% distribution from a portfolio invested on a total return basis and you would not have to worry about growing your reserves.

These are obviously only a few suggestions for consideration.  But you might try them out on a knowledgeable lawyer who can review your full financial situation, your present program, and your desires for the future.  There are probably several possible options.