Move biblatex category headings into left marginpar

Question

I'm trying to move the alphabetical category headers into the left marginpar. I followed this post for ordering the bibliography alphabetically and that worked well. I was able to use marginpar instead of a section header, but they appear in the wrong line and there is additional space between the categories. The relevant code is

\renewcommand*{\do}[1]{\defbibheading{#1}{\marginpar[left]{\hfill #1}}}

It does make sense that the marginpar floats on the previous line, as that's where bibheading is called, but I cannot make sense of the spacing. There does not seem to be any combination of \baselineskip, \bibitemsep or \bibinitsep of vspace between the categories. When I move the marginpar down by adding a \vspace{FANTASY_DIM} it only sporadically lines up with the first category entry.

This is the atrocity that my current code produces:

I want the category marginpars to line up with it's first entry and even spacing between all the bibliography entries (no extra space between categories). For my bibliography I currently use biblatex with the natbib=true option-

Answer 1

If you just want the letter in the margin, you don't need to go via bibliography categories and headings.

As in the answers to the linked questions, we make use of the sortinit field. The idea is to remember the sortinit of the last entry and compare it to that of the current entry. If the two differ, we print the field. Now we only need the field format to push things into the margin. You can use \marginpar for that or you use a homebrew macro.

\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber, style=authoryear]{biblatex}
\makeatletter
\DeclareFieldFormat{margin:sortinit}{\printinmargin{\mkbibbold{#1}}}
\AtBeginBibliography{\global\undef\bbx@prevsortinit}
\providebool{bbx@inset}
\renewbibmacro{begentry}{%
  \ifbool{bbx@inset}
    {}
    {\iffieldequals{sortinit}\bbx@prevsortinit
       {}
       {\printfield[margin:sortinit]{sortinit}%
        \savefield{sortinit}\bbx@prevsortinit}}%
}
% inspired by egreg's (https://tex.stackexchange.com/users/4427/egreg)
% answer to https://tex.stackexchange.com/a/123451/35864
\newcommand{\printinmargin}[1]{%
  \strut\vadjust{\printinmargin@i{#1}}}
\newcommand{\printinmargin@i}[1]{%
  \vbox to 0pt{%
    \kern-\dimexpr\dp\strutbox+\ht\strutbox\relax
    \strut
    \hfill
    \rlap{\kern1.5em #1}%
    \vss
  }%
}
\makeatother
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{sigfridsson}
\nocite{*}
\printbibliography
\end{document}