Technically, you can give money to a federal agency, but (with few exceptions) they in turn have to forward the money to the Treasury for the general fund.
So work with the pizza place to get a special 95% discount then hand them cash "not related to the order". For something that's obviously a good faith contribution everyone involved will err toward the side of rubber stamping it as ok.
The rules are just a rule of thumb that we can apply evenly at scale to avoid corruption. When there's legitimately no corruption happening the rules get more flexible. If it ever becomes an issue HR will frown (because rules) but legal will apply the duck test and conclude that ~$10 pizza/person paid for by someone who doesn't need/want/isn't in a position to benefit from preferential treatment is not corruption.
NASA contractor here. Our funding has been slowly declining in recent years, with some years better than others. It's currently about 20 billion USD, or about 0.5% of the US budget. We are not what I would call "quite well funded", but we manage. A project I support, WFIRST, is currently over budget (as most space telescopes have been) and is constantly under threat of being cancelled. The recent shutdown cost the Government far more that what is needed to finish WFIRST.
Details of the NASA budget can be found at the inevitable Wikipedia page:
"The artist’s share of profits from sales of this poster will be donated to NASA."
How, Though? You can't donate to NASA