Sane footnotes in beamer: per frame numbering and several in a row

Question

It is absurdly hard to get this right:

in a Beamer presentation, I wish that footnotes:

1. are numbered per frame
2. are laid out without stacking, i.e., several by row

Supposedly, the footmisc package which options perpage and para would solve these two problems, respectively. Also, adding [frame] to the footnote commands is necessary for a decent layout (just try without it...).

But:

1. the para option produces no effect, silently;

2. the perpage option causes an error, when the [frame] option is given to \footnote:

    ! Missing number, treated as zero.
    <to be read again> 
                       f
    l.36 \end{frame}
   

I read somewhere here that footmisc is incompatible with hyperref, which is loaded by default by beamer, so is there any hope? Putting \RequirePackage[para,perpage]{footmisc} before the \documentclass yields a whole set of new problems, so, how are people achieving this? Are they actually writing footnotes by hand? It does not seem unreasonable to need multiple bibliographical references by frame, let's say in a PhD defense introduction.

---

Minimal Working Example

\documentclass[a4paper, aspectratio=169]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
%\usetheme{metropolis}
\usepackage[para]{footmisc} % Multiple footnotes on one page.
                            % Add 'perpage' to break stuff.
% This is supposed to fix a failure of footmisc[perpage] combined with hyperref: https://tex.stackexchange.com/a/40091/
%\newcommand\fnsep{\textsuperscript{,}} % put this between consecutive footnotes
% Optional footnote styling
\setbeamerfont{footnote}{size=\scriptsize}
\renewcommand\thefootnote{\textcolor{gray}{\arabic{footnote}}}
%\let\origfootnote=\footnote
%\renewcommand\footnote[2][frame]{\origfootnote[#1]{\textcolor{gray}{#2}}}
\let\origfootnoterule=\footnoterule
\renewcommand\footnoterule{\textcolor{black!30}{\origfootnoterule}}
\title{My Title}
\author{I. Myself}
\date{\today}
\begin{document}
\begin{frame}{}
    \begin{columns}
        \begin{column}{.5\linewidth}
            Thing\footnote[frame]{Doe et al. 1987}
        \end{column}
    \begin{column}{.5\linewidth}
        Next thing\footnote[frame]{Smith et al. 2012}
    \end{column}
\end{columns}

\end{frame}
\begin{frame}{Footnotes numbers should start at one on each frame}
    One last thing\footnote[frame]{first footnote on this the frame}
\end{frame}
\end{document}