Is there meila on the para aduma and mei chatas and is it debatable if the entire avoda and tahara of the para aduma was a function of hekdesh? Is it possible that it's simply a communal process that was performed by a kohein but really wasn't part of kodshim?

I know about the gemara that says that it's kdushas bedek habayis but I have a way to deflect that rayah. Any other rayos one way or the other?