Limitations of TikZ Braids: Are there alternatives?

Question

I've been using the Tikz braids package which is all nice and great, but it's also limiting in that there seems to be only one way to generate braids. For example, I think a lot of people like to draw braids like this (apologies for the blurriness; was trying to avoid an oversized image):

(This is from Fresse's Homotopy of Operads.) However, the braids package is designed to show you, one at a time, the action of every single generator. This is great for pedagogy! But complicated braids have lots of generators. As a result, complex braids get really long. For example, I hand drew the braid on the left. Plugging it into the braids package, I get the picture on the right

Issues.

My issue is that (1) the braid doesn't fit on a single page. Now I can use adjustbox to scale it to make it fit, but this brings my second issue: it makes the braid look more complicated than it really needs to be.

Questions.

So my questions are: Is this really all that the TikZ braids package can do? I looked at the documentation and it seems to be the case. In addition, are there other alternatives to generating braids in TikZ? How are other authors (e.g. Fresse above) generating their braids? Are they really just hardcoding a tikzpicture every time?

Also, there's this question but this just looks like a nightmare to do in general. In my experience with TikZ it often requires way too much time to just generate something pretty simple, so I don't want to hard code it (if I can avoid it!!).

Finally, I don't know if it helps, but heres my code for the above braid.

\begin{tikzpicture}
\braid[number of strands= 9, thick,
style strands={1}{red},
style strands={2}{red},
style strands={3}{red},
style strands={4}{Green},
style strands={5}{Green},
style strands={6}{Black},
style strands={7}{RoyalBlue},
style strands={8}{RoyalBlue},
style strands={9}{RoyalBlue}] 
(braid) 
s_3 s_2 s_1 s_4 s_3 s_2
s_6 s_7 s_8 
s_5 s_4 s_3 s_6 s_5 s_4 s_7 s_6 s_5
s_5 s_4 s_3 s_6 s_5 s_4 s_7 s_6 s_5;
\end{tikzpicture} 

Answer 1

\documentclass{article}
%\url{https://tex.stackexchange.com/q/549289/86}
\usepackage{tikz}
\usetikzlibrary{braids}


\begin{document}

\begin{tikzpicture}
\pic[
  braid/.cd,
  every strand/.style={ultra thick},
  strand 1/.style={red},
  strand 2/.style={red},
  strand 3/.style={red},
  strand 4/.style={green},
  strand 5/.style={green},
  strand 6/.style={black},
  strand 7/.style={blue},
  strand 8/.style={blue},
  strand 9/.style={blue},
  control factor=.001,
  nudge factor=.001,
  height=-.8cm
  ]
{braid={%
s_3-s_6
s_2-s_4-s_7
s_1-s_3-s_5-s_8
s_2-s_4-s_6
s_3-s_5-s_7
s_4-s_6
s_5
s_5
s_4-s_6
s_3-s_5-s_7
s_4-s_6-s_8
s_5-s_7
s_6
}};
\end{tikzpicture}

\end{document}

If you reach the limitations of the braids package, try the knots package.