Sorting Icelandic index correctly using LaTeX (accented characters after non-accented)

Question

I'm using Xindy to make an index for my book. It sorts the words mostly correctly, but it doesn't sort accented characters (i.e. á é í ó ú ý) after the corresponding non-accented characters (a e i o u y), unless the words are otherwise identical. For example, Xindy will sort 'ís' after 'is', but it will sort 'auga' after 'ás'. I would like it to sort ás after auga, and in general I want it to sort the accented characters after the corresponding non-accented character. For the record, this is the correct sort order:

a, á, b, c, d, ð, e, é, f, g, h, i, í, j, k, l, m, n, o, ó, p, q, r, s, t, u, ú, v, w, x, y, ý, z, þ, æ, ö

Here's my MWE:

% filename alphabet.tex
\documentclass[a4paper,11pt]{book}
\usepackage[icelandic]{babel}
\usepackage[T1]{fontenc}
\usepackage{makeidx}
\makeindex

\title{My book}
\author{Me}
\begin{document}
\chapter{Stafrófið}

Ananas\index{ananas}, ás\index{ás},
banani\index{banani}, dagblað\index{dagblað}, epli\index{epli}, ég\index{ég}, flugvél\index{flugvél}, gíraffi\index{gíraffi}, hús\index{hús}, indíáni\index{indíáni}, ís\index{ís}, jörðin\index{jörðin}, kisa\index{kisa}, lykill\index{lykill}, mús\index{mús},
nef\index{nef}, ormur\index{ormur}, óbó\index{óbó}, píanó\index{píanó}, rós\index{rós}, skæri\index{skæri}, tré\index{tré}, ugla\index{ugla}, úr\index{úr}, varir\index{varir}, yddari\index{yddari}, ýta\index{ýta}, þvottavél\index{þvottavél}, æð\index{æð}, ör\index{ör}, auga\index{auga}, eyra\index{eyra}.

\printindex
\end{document}

I compile it using

pdflatex alphabet.tex
texindy -L icelandic alphabet.idx
pdflatex alphabet.tex

(you may have to update Xindy, as I had to do). What I'm hoping for is some kind of command, either in my .tex document or in some file that Xindy reads, but other solutions are appreciated.

This question is similar and has an answer that seems to work but it uses LuaTex while I use LaTeX (switching is not an option). It's also very long and technical for such a (seemingly) simple change.

Edit: I failed to mention that my LaTeX file is not utf-8 encoded and I'm not using \usepackage[utf8]{inputenc}, which I think might matter. I'm working on a 300+ book and I'm afraid that changing the encoding might have unexpected effects, so if there's a solution that doesn't require utf-8, that would be preferred.

Answer 1

The solution can be found at question Texindy sorting Icelandic - Edit 2 A minimalistic version and LuaTex is not required to obtain the solution.

Download the first file using a terminal and place it inside your LaTex folder:

wget http://striz7.fame.utb.cz/tex-sx/is-min/icelandicmalmin.xdy  

Update: Download iec2utf and place all files inside your LaTex folder:

https://github.com/michal-h21/iec2utf

Run the following commands:

pdflatex alphabet
texlua iec2utf.lua <alphabet.idx >mal-temp.idx
xindy -M texindy -M icelandicmalmin-test -M mal-style -o alphabet.ind mal-temp.idx
biber alphabet
pdflatex alphabet
pdflatex alphabet

Example of index sorting Icelandic characters with accents: