I actually sort of agree with this notion, even though part of me thinks it's evil.
Here's a direction (not a solution since I don't actually like it as a suggestion): What if the ticket sales of the relegation playoff had to be shared with the 5th place teams. Perhaps the home team gets 50%, the visiting team gets 25%, and the 5th place team gets 25%. The 5th place team would get the cut from the games either of the 6th place team in its own conference or home games in conference arenas (probably the latter). This idea would both give the 5th place team a sliver of income while taking that sliver from the income of the 6th and 7th place teams.
I personally don't like this idea specifically (even though I'm throwing it out there), but maybe there's a thread of the idea to pull on that might lead to some brilliant revelation.
Don't ask what sort of Chunks they are, you probably don't want to know. Blowing Chunks since Season 4!