TikZ-Roulette: Make animation more realistic

I followed a slightly different approach from @samcarter's and just assumed that the angular velocity decreases linearly from some maximal value vmax to zero. Then I integrated the angular velocity to get an angle. Sorry, I had to shorten your code a bit to produce a gif that can be uploaded. Unfortunately, I do not know how to upload mp4 files, which can be produced as described in this other answer by @samcarter.

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\pgfmathsetmacro{\Frame}{0}
\tikzset{declare function={tmax=100;
vmax=40;
rot(\t)=(\t/2)*(2-\t/tmax)*vmax;}}
\foreach \Frame in {0,...,100}
{\begin{tikzpicture}
\foreach \Y [evaluate=\Y as \X using {10*\Y+rot(\Frame)}] in {0,...,35}
{
\ifodd\Y
\fill (\X-5:2.5) -- (\X-5:2) arc(\X-5:\X+5:2) -- (\X+5:2.5) arc(\X+5:\X-5:2.5);
\node[rotate=\X] at (\X:2.75){\Y};
\else
\fill[red] (\X-5:2.5) -- (\X-5:2) arc(\X-5:\X+5:2) -- (\X+5:2.5) arc(\X+5:\X-5:2.5);
\node[rotate=\X,red] at (\X:2.75){\Y};
\fi
\draw (\X-5:2.5) -- (\X-5:3) arc(\X-5:\X+5:3) 
-- (\X+5:2.5) arc(\X+5:\X-5:2.5);
}
\shade[ball color=gray] ({-rot(\Frame)}:2.25) circle (1mm);
\end{tikzpicture}}
\end{document}

For the part of your question about the slowing down:

A simple solution would be to write a wrapper document that displays each page of your animation an increasing number of times.

For example if your animation creates 16 pages, the following document will show the first page one time, the second page two times etc. You could also use other functions, this linear function is just an example:

\documentclass{beamer}

\setbeamertemplate{navigation symbols}{}
\usepackage{tikz}

\definecolor{filz}{RGB}{56,114,73}
\setbeamercolor{background canvas}{bg=filz}

\begin{document}

\foreach \n in {1,...,16}{

\begin{frame}[plain]
\foreach \x in {1,...,\insertframenumber}{
\includegraphics<+>[height=\paperheight,page=\insertframenumber]{document}}
\end{frame}

}

\end{document}

(sorry for the tiny image, the .gif would otherwise be too big to upload)