Let me start by saying what I know about GREP I learned here from Jongware and Peter Kahrel, and from Peter's book, which I highly recommend.
Eiher one of them may come along with a better solution as soon as I'm done, but in the meantime I think the lookarounds don't work because the lengths could be variable. I do have an alternate plan that DOES seem to work, however, and eliminates the need to use the clipboard as a bonus.
Use the search expression
(\~hl [^\~]+)(\~he [^\~]+)(\~hd [^\~]+)(\~hf [^\~]+)(\~hb [^\~]+)
and then use a sequence of $1 through $5 to rearrange the order, for example $1$2$5$3$4 will move the ~hb paragraph after the ~he and before the ~hd.
I thought you would need (?s), which is the "single line" marker that causes the entire story to be treated as a single paragraph at the beginning of the query, but that doesn't seem to be the case. Also, spaces and returns are bicked up by the [^\~] (not a tilde) class, so you don't need to explicitily include them unless you want to be sure that they are in precise positions, like the space after the ~hl. I left those in, but there is no point in leaving in the the \r as it cannot be used with the negative class to stop the match unless the return itself is included in the class. This leaves the possibility that you could have intervening paragraphs that don't start with a tilde, and they would be considerd, as far as a match, as belonging with whatever paragraph starting with a tilde comes before them.
If you want the query to not match any paragraph that doesn't start with a tilde (in other words it should fail if there is an intervening pargargraph in the list without the prefix), I think you could modify it as follows:
(\~hl [^\~\r]+\r)(\~he [^\~\r]+\r)(\~hd [^\~\r]+\r)(\~hf [^\~\r]+\r)(\~hb [^\~\r]+\r)
which also will not match if your ~hb paragraph is the last in the story and does not have a trailing return. In the first query it is found, which can lead to combining it with another paragraph (I know this because it happened in my test).