Syntax:
\bottompar[<symbol>]{<content>}
where
<symbol> is an optional marker. If unspecified, a letter is used i.e. a for the first, then b etc.
<content> is contents to be appended to the bottom note for this page.
If used multiple times on a single page, the content is accumulated and the notes are set as a single paragraph at the bottom. Paragraph breaks may be added, but are not created.
Aside from the symbol or letter, \bottompar adds a small amount of space between each separate addition to its content.
At the end of the page, the accumulation of material is typeset and the settings are cleared, except that the counter used to keep track of which letter to use as a marker is not reset.
\documentclass{memoir}
\usepackage{lipsum}
\medievalpage
\checkandfixthelayout
\sideparmargin{outer}
% ateb: https://tex.stackexchange.com/a/735227/
% addaswyd o gwestiwn Matt Petersen: https://tex.stackexchange.com/q/735217/
\ExplSyntaxOn
\coffin_new:N \g__bottompar_note_coffin
\tl_new:N \g__bottompar_content_tl
\cs_new_protected:Npn \__bottompar_make:
{
\tl_if_empty:NF \g__botttompar_content_tl
{
% change the width of the bottompars on the next line
\vcoffin_gset:NnV \g__bottompar_note_coffin { 0.5\foremargin + \linewidth } \g__bottompar_content_tl
\tl_gclear:N \g__bottompar_content_tl
}
}
\cs_generate_variant:Nn \vcoffin_gset:Nnn { NnV }
\cs_new:Npn \__bottompar_do:
{
\coffin_typeset:Nnnnn \g__bottompar_note_coffin { t } { l } { 0pt } { 0pt }
\coffin_gclear:N \g__bottompar_note_coffin
}
\cs_new_eq:NN \makebottompar \__bottompar_make:
\cs_new_eq:NN \dobottompar \__bottompar_do:
\hook_gput_code:nnn { begindocument } {bottompar}
{
\hook_gput_code:nnn {shipout/foreground} {bottompar}
{
% typeset the bottompar into a coffin and clear the token list
\makebottompar
% the next line determines where the top left corner of the bottom par is placed
% this is half the foremargin to the right of the far left of the page (horizontal)
% and the total of the upper margin, text height, header height and header sep from the top
\put (\dimexpr 0.5\foremargin, \dimexpr -\uppermargin-\textheight-\headheight-\headsep) {
% typeset and clear the coffin
\dobottompar
}
}
}
\int_new:N \g__bottompar_no_int
\NewDocumentCommand \bottompar { o +m }
{
\tl_if_empty:NT \g__bottompar_content_tl
{
\tl_gset:Nn \g__bottompar_content_tl { \hskip -0.5em }
}
% create marker and append to token list
\IfValueTF { #1 } {
\tl_gput_right:Nn \g__bottompar_content_tl { \hskip 0.5em \textsuperscript{ #1 } }
\textsuperscript { #1 }
} {
\int_gincr:N \g__bottompar_no_int
\textsuperscript { \int_to_alph:n { \g__bottompar_no_int } }
\tl_gput_right:Ne \g__bottompar_content_tl {
\hskip 0.5em \noexpand\textsuperscript { \int_to_alph:n { \g__bottompar_no_int } }
}
}
% append the content of the bottom par to the token list
\tl_gput_right:Nn \g__bottompar_content_tl { #2 }
}
\ExplSyntaxOff
\begin{document}
\sidepar{\footnotesize\lipsum[8]}\lipsum[1]\bottompar{% did you really want a space here?
\lipsum[6-7]% or here?
}
\lipsum[2-5]
A paragraph with a footnote\footnote{A regular, common-or-garden footnote of the ordinary kind. \lipsum[10]}
\lipsum[8-9]
\sidepar{\footnotesize\lipsum[8]}\lipsum[1]\bottompar{%
\lipsum[11]%
}
Something else\bottompar{Another bottom one.}
Furthermore\bottompar[\textdagger]{A bottom note with a custom symbol.}
However\bottompar{Perhaps letters are best.}
\end{document}

I couldn't remember exactly what the various dimensions specify in terms of the layout and I wasn't able to determine this immediately from the manual, so I just guessed and did it by trial-and-error. So positioning may need fine-tuning. Also, I wasn't sure how wide the note should be, so you may need to modify that according to your desiderata.
strictpagecheck.)flowframwithmemoir. are you OK with checking things fit manually? (you would get a warning in the log, but the bottom-note wouldn't move to another page.) if so, you could just add them into the shipout hook. unlike margin notes, you don't even need to remember a position - you've got a fixed point on the page.