How get hyperref links to 2nd bibliography with multibib and amsplain bibtex style?

Question

Is it possible to get hyperref hyperlinks on a 2nd bibliography with the multibib package and the amsplain BibTeX style?

Example:

\documentclass[12pt]{article}

\usepackage{multibib}
\newcites{two}{More Information}

\usepackage{hyperref}
\hypersetup{hyperindex,colorlinks, citecolor=red} 

\begin{filecontents}{main.bib}
@article{Archimedes200,author = {Archimedes},title = {Pi's the limit },
journal = {Rome J. Gastronomical Math.}, year = {200BCE},volume = {10},pages={\textsc{CCCXV}--\textsc{CCCXIV}}}

@article{EulerE1776,Author = {Euler, Leonhard},Title = {All about E},
Journal = {Popular Math.},Year = {1776},Volume = {4},pages={1--2718}}
\end{filecontents}

\begin{filecontents}{second.bib}
@book{BourbakiSets1970,Author={Bourbaki, Nicolas},Title={Th{\'e}orie des ensembles},
Year={1970},Publisher={Hermann},Location={Paris}}
\end{filecontents}

\makeindex

\begin{document}

Archimedes~\cite{Archimedes200} and Euler~\cite{EulerE1776} studied the constants, $\pi$ and $e$, respectively.

Bourbaki~\citetwo{BourbakiSets1970} treats set theory axiomatically.

\bibliographystyle{amsplain}
\bibliography{main}
\bibliographystyletwo{amsplain}
\bibliographytwo{second}

\end{document}

Other posts propose solving this either by using natbib (e.g., multibib - hyperref doesn't work for my second bibliography) or biblatex (e.g., Problem in combining hyperref with multibib).

However, I am wedded to the amsplain bibtex style, which does not seem to be available with either natbib or biblatex.

Is there some workaround? Even hacks to hyperref or multibib would be OK (although, of course, not preferable).

Partial solution

Following the helpful suggestions by @jon, the following modified source does use biblatex to create two bibliographies, with hyperlinks to each from hyperref. The two bibliographies are independent, as I want; and no mods are needed in the source .bib files. I have not yet tackled the issue of modifying the bib style so as to resemble amsplain.

However, the 2nd printed bibliography resets the counter at 1, despite my attempt to manually reset it.

Is there a way to continue numbering in the 2nd bibliography after where the numbering in the 1st bibliography ends?

\documentclass[12pt]{memoir}

\usepackage[style=numeric,backend=bibtex]{biblatex}

\usepackage{hyperref}
\hypersetup{hyperindex,colorlinks, citecolor=red} 

\begin{filecontents}{main.bib}
@article{Archimedes200,author = {Archimedes},title = {Pi's the limit },
journal = {Syracuse J. Gastronom.\ Math.}, year = {200BCE},volume = {10},pages={\textsc{CCCXV}--\textsc{CCCXIV}}}

@article{EulerE1776,Author = {Euler, Leonhard},Title = {All about E},
Journal = {Math.\ Psychol.},Year = {1776},Volume = {4},pages={1--2718}}
\end{filecontents}

\begin{filecontents}{two.bib}
@book{BourbakiSets1970,Author={Bourbaki, Nicolas},Title={Th{\'e}orie des ensembles},
Year={1970},Publisher={Hermann},place={Paris}}
\end{filecontents}

\addbibresource{main.bib}
\addbibresource{two.bib}

\begin{document}

Archimedes~\cite{Archimedes200} and Euler~\cite{EulerE1776} studied the constants, $\pi$ and $e$,  respectively.

\printbibliography % main

\newrefsection
\defbibnote{readprenote}{Here are some suggested readings.}
\printbibliography[title={Additional Readings},resetnumbers=3,prenote=readprenote] % two 

Bourbaki~\cite{BourbakiSets1970} treats set theory axiomatically.

\end{document}

Fix for 2nd bibliography numbering

Using the refsegment environment from biblatex, instead of \newrefsection, and adding the defernumbers=true option when loading biblatex, seems to fix the numbering problem: by default, numbering of the 2nd bibliography resumes with the next number after the last number in the 1st bibliography.

Here's the complete source again but with that modification:

\documentclass[12pt]{memoir}

\usepackage[style=numeric,backend=bibtex,defernumbers=true]{biblatex}    
\usepackage{hyperref}
\hypersetup{hyperindex,colorlinks, citecolor=red} 

\begin{filecontents}{main.bib}
@article{Archimedes200,author = {Archimedes},title = {Pi's the limit },
journal = {Syracuse J. Gastronom.\ Math.}, year = {200BCE},volume = {10},pages={\textsc{CCCXV}--\textsc{CCCXIV}}}

@article{EulerE1776,Author = {Euler, Leonhard},Title = {All about E},
Journal = {Math.\ Psychol.},Year = {1776},Volume = {4},pages={1--2718}}
\end{filecontents}

\begin{filecontents}{two.bib}
@book{BourbakiSets1970,Author={Bourbaki, Nicolas},Title={Th{\'e}orie des ensembles},
Year={1970},Publisher={Hermann},place={Paris}}
\end{filecontents}

\addbibresource{main.bib}
\addbibresource{two.bib}

\begin{document}

\begin{refsegment} 

Archimedes~\cite{Archimedes200} and Euler~\cite{EulerE1776} studied the constants, $\pi$ and $e$,  respectively.

\end{refsegment}

\printbibliography[segment=1] % main

\defbibnote{readprenote}{Here are some suggested readings.}
\printbibliography[title={Additional Readings},prenote=readprenote,segment=2]

\begin{refsegment}

Bourbaki~\cite{BourbakiSets1970} treats set theory axiomatically.

\end{refsegment}

\end{document}

Notice that this works even though the citations to the 2nd bibliography appear after it is printed.