Does the Holy Cross interment listing give any name other than Anthony Mullen? I see that Catherine Loftus owned it; what I'm looking for is any other clue.
Did someone go to the cemetery to look for the grave? I was there yesterday and hope to head back over the summer. I can look then; the only way to do so is to use what you've provided as this cemetery is HUGE.
In looking over this thread, there is no indication that Anthony died in Philadelphia. He was buried there, but in my experience, it's not uncommon for someone to die in one state or county but be buried in another. You might want to try contacting the state again. Here's what I would do (though I've no done it and don't know if it would work): make a copy of the no record found response, make a note on it that he was BURIED in Delaware County, and ask if they would have a record for transporting the body. They may not look again, but you'll have only lost the cost of a stamp and ruled out a source in the process.
The Philadelphia Free Library is still active and open. They have raised the price on obits, but they continue to do the lookups. It now costs $10 as opposed to 2 or 3, but it's an excellent resource.
The bad news in your search is that you're working in a time frame that's not easily researched as newspapers online stop at mid-1922 in Philadelphia. The Philadelphia City Directory is published less frequently by now, and the vital records are not allowed to be viewed by the public after mid-1915. With no spouse or children to search for, there's little to work with now, but it is still doable, just a bit more challenging. If you have information that you aren't comfortable posting publicly or that is recent, please feel free to send me a PM.