How could one have three columns of footnotes which do not go over the page with three columns of text?

Question

I wish to place three columns of body text above three columns of footnotes. In all other respects, the footnotes should behave the same way as normal footnotes, that is, they should not differ from the output produced by \footnote. This would include the automatic avoidance of text overflow. I do not mind if footnotes do not exactly match with their columns; that is, I do not mind if all the footnotes are bunched together as a separate text and then displayed below in three columns, such that footnotes from the second column may, if there are no or few footnotes from the first column, appear in the first column of the footnote area.

This question is likely a duplicate of a previous question, with a slight variation. However, it has no answers, and there has been no activity since 2014. Having asked chat, I decided to post a new question; I apologise if I shouldn't have. Someone else suggested offering a bounty; I have not proved so competent as to acquire enough reputation to do this, so I can't.

Achieving a three column layout appears relatively trivial, using multicols, as documented here.

I have also seen a number of ways of achieving a three column footnote layout. However, they each seem to be problematic in combination with multicols.

1. memoir with \threecolumnfootnotes*

   Consider this example:

   \documentclass{memoir}
   
   \threecolumnfootnotes
   
   \begin{document}
   
   \null\vfill% just for the example
   
   Some text.\footnote{Author 2001} Some more text.\footnote{Buthor 2002}
       And some more.\footnote{Cuthor 2003} Does this text ever end?\footnote{Duthor 2004}
       Yes.\footnote{Euthor 2005}
   
   \end{document}
   

   Upon adding multicols, things initially seem to work a little, but the footnotes seem to have newlines in odd places:

   

   When we add some text from lipsum, the following occurs:

   

2. ledmac* appears to be deprecated, and there is no example with reledmac. I suspect the same issue would apply here anyway, given the answer says that memoir is "based on ... ledmac". A comment below (from the original author of both) says that this is false. I shall update this question to reflect that shortly.

3. bidi* also appears not to work. Consider the following example:

   \documentclass[10pt,a4paper]{memoir}
   \usepackage[utf8]{inputenc}
   \usepackage{lipsum}
   \usepackage{multicol}
   
   \usepackage[extrafootnotefeatures]{bidi}
   \threecolumnfootnotes
   
   \begin{document}
   
   \begin{multicols}{3}
   
   \lipsum
   \footnote{Pater noster, qui es in caelis, sanctificetur nomen tuum. Adveniat regnum tuum. Fiat voluntas tua, sicut in caelo et in terra. Panem nostrum quotidianum da nobis hodie, et dimitte nobis debita nostra sicut et nos dimittimus debitoribus nostris. Et ne nos inducas in tentationem, sed libera nos a malo. Amen.}  
   
   \end{multicols}
   
   \end{document}
   

   Initially, we have something which appears to work.

   

   If, however, we have more footnote text, it fails.

   

4. footmisc with para**.

   The para option with footmisc does something different to what is sought in this question. Where there are multiple footnotes, they can be displayed on the same line, or on separate lines. para achieves the former; it does not ensure that lines display side by side.