Of course spending the money more efficiently would be preferable, but additional resources spent the same way would also work.
We are already spending, as a nation, much more than this. We spend roughly $3B federally directly on homelessness (not including other programs aimed at poverty that provide assistance). California spends $1B. California localities spend $3B. New York City spends $3B alone.
These are just governmental expenditures, aimed directly at homelessness, and ignore charitable efforts.
One caveat with the analysis is that your census of homeless people does not count the people housed as a result of these programs. It also doesn't count the number of people that would have to be served that are not presently considered homeless.
Ideally federal agencies should take care of this and make sure that every US citizen in need is taken care of where he lives.
Yes, there are circumstances where throwing someone on a bus to a locality where he has some family or other connections is the best move for all involved. But we need to make sure that is actually the case, not based on some tenuous connection and a desire to displace the costly individual somewhere else.
This isn't enough, though. Even without explicit governmental support to move, homeless people know that there are localities where it's "better" to be homeless and will move themselves.
That is close to impossible, I'm afraid. And even if federal regulation prohibits the executive branch from such programs, I guarantee that it will be replaced by some "church", neighborhood watch, political action group or whatever...
e.g. The City of San Francisco is spending over $300M/year directly on services towards easing homelessness. This does not count state expenditures focused in the area, private expenditures, expenditures by surrounding areas, and the wealth of indirect expenses. Versus a homeless population of 10,000, this is $30,000 per year per homeless person in the City of SF-- just direct expenses by City of SF.
Clearly an overall change in approach is needed-- not just additional resources spent the same way.