biblatex doesn't really do 'freeform' citations. The whole point of biblatex (and BibTeX) is that you feed it with all semantically meaningful bits of information separately so that those bits can be reassembled according to a scheme defined by a chosen bibliography and citation style.
If you can find a common structure for a subclass of your citations you may be able to come up with a scheme to classify them and decompose the various data into handy bite-sized chunks that biblatex can deal with. You could then write your own entry type as described in How can I create entirely new data types with BibLaTeX/Biber?.
Here is an atrocious hack that takes the strategy you have been using slightly further and gives you the output you want.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=verbose, backend=biber]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{marriage,
shorthand = {Church of England (Derby, Derbs.), Parish Registers, vol.\ 4, p.\ 3, Smith-Bloggs (20 January 1815).},
note = {\ifcitation
{Church of England (Derby, Derbyshire, England), Parish Registers, vol.\ 4, p.\ 3, marriage of John Smith and Jane Bloggs (20 January 1815); digital images, Ancestry.com (\url{http://ancestry.com.au}: accessed 1 July 2018), citing Derbyshire Record Office, Matlock.}
{Church of England (Derby, Derbyshire, England). Parish Registers. Digital images. Ancestry.com. \url{http://ancestry.com.au}: 2018.}},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\renewbibmacro*{shorthandintro}{}
\begin{document}
Lorem\footcite{marriage} ipsum\footcite{marriage}
\printbibliography
\end{document}
But if we are doing that we might as well stop and abuse fields and declare our own 'freeform' citations.
This is a first shot at a @freeform entry type for the verbose styles.
It supports the field bibliography for the display in the bibliography, firstcite for the first longer citation and cite for subsequent citations. The field sortkey can be used to give the sorting position in the bibliography.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage{filecontents}
\begin{filecontents}{freeform.dbx}
\DeclareDatamodelEntrytypes{freeform}
\DeclareDatamodelFields[type=field,datatype=literal]{
bibliography,
cite,
firstcite,
}
\DeclareDatamodelEntryfields[freeform]{
bibliography,
cite,
firstcite,
sortkey,
}
\end{filecontents}
\usepackage[style=verbose, backend=biber, datamodel=freeform, mincrossrefs=1]{biblatex}
\DeclareBibliographyDriver{freeform}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\printfield{bibliography}%
\setunit{\bibpagerefpunct}\newblock
\usebibmacro{pageref}%
\newunit\newblock
\iftoggle{bbx:related}
{\usebibmacro{related:init}%
\usebibmacro{related}}
{}%
\usebibmacro{finentry}}
\renewbibmacro*{cite:full}{%
\ifentrytype{freeform}
{\iffieldundef{firstcite}
{\usebibmacro{cite:short}}
{\printfield{firstcite}}}
{\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}}
\renewbibmacro*{cite:short}{%
\ifentrytype{freeform}
{\printfield{cite}}
{\printnames{labelname}%
\setunit*{\printdelim{nametitledelim}}%
\printtext[bibhyperlink]{%
\printfield[citetitle]{labeltitle}}}}
\DeclareSourcemap{
\maps[datatype=bibtex,overwrite=false]{
\map{
\pertype{freeform}
\step[fieldsource=bibliography]
\step[fieldset=sortkey, origfieldval]
}
}
}
\begin{filecontents}{\jobname.bib}
@freeform{marriage,
cite = {Church of England (Derby, Derbs.), Parish Registers, vol.\ 4, p.\ 3, Smith-Bloggs (20 January 1815).},
firstcite = {Church of England (Derby, Derbyshire, England), Parish Registers, vol.\ 4, p.\ 3, marriage of John Smith and Jane Bloggs (20 January 1815); digital images, Ancestry.com (\url{http://ancestry.com.au}: accessed 1 July 2018), citing Derbyshire Record Office, Matlock.},
bibliography = {Church of England (Derby, Derbyshire, England). Parish Registers. Digital images. Ancestry.com. \url{http://ancestry.com.au}: 2018.},
sortkey = {Church of England, Derby, Derbyshire, England},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Lorem\footcite{marriage} ipsum\footcite{marriage}
\printbibliography
\end{document}

If you have two entries with the same bibliography you will of course get that output twice in the references, which may look odd. If you don't want that you can make sure that the same bibliography is only shown once by using a more complex structure in the .bib file.
@freeform{marriage:smithbloggs,
cite = {Church of England (Derby, Derbs.), Parish Registers, vol.\ 4, p.\ 3, Smith-Bloggs (20 January 1815).},
firstcite = {Church of England (Derby, Derbyshire, England), Parish Registers, vol.\ 4, p.\ 3, marriage of John Smith and Jane Bloggs (20 January 1815); digital images, Ancestry.com (\url{http://ancestry.com.au}: accessed 1 July 2018), citing Derbyshire Record Office, Matlock.},
options = {skipbib},
crossref = {coe:derb},
}
@freeform{marriage:smothbliggs,
cite = {Church of England (Derby, Derbs.), Parish Registers, vol.\ 5, p.\ 1, Smoth-Bliggs (30 April 1815).},
firstcite = {Church of England (Derby, Derbyshire, England), Parish Registers, vol.\ 5, p.\ 1, marriage of Jane Smoth and John Bliggs (30 April 1815); digital images, Ancestry.com (\url{http://ancestry.com.au}: accessed 1 July 2018), citing Derbyshire Record Office, Matlock.},
options = {skipbib},
crossref = {coe:derb},
}
@freeform{coe:derb,
sortkey = {Church of England, Derby, Derbyshire, England},
bibliography = {Church of England (Derby, Derbyshire, England). Parish Registers. Digital images. Ancestry.com. \url{http://ancestry.com.au}: 2018.},
}
If two entries share the same bibliography, you can outsource the bibliography and sortkey fields into a new entry and reference it from the citation entries with crossref = {...}, make sure that the citation entries don't end up in the bibliography with options = {skipbib},.
But here biblatex does not really do a lot except for sorting and tracking of first vs. subsequent citations. That could be achieved differently.
shorthandfield in my.bibfile. – S. Bell Jul 01 '18 at 10:01biblatexis not really great with 'freeform' citations. The whole idea is that you give all semantically meaningful bits of information separately, so that they can be reassembled according to a particular style. Depending on your exact requirements hacks are available, but that can easily get out of hand or ugly. Can you add your example to your question along with all the three forms you would expect to be made from it. – moewe Jul 01 '18 at 10:10biblatexbut it seemed as good an option as any from my limited experience. I have added the three modes of an example 'freeform' citation. – S. Bell Jul 01 '18 at 10:20biblatexmight be useful, it could be easier to try something else... – moewe Jul 01 '18 at 10:30biblatex... I'm just looking for as simple and efficient a solution as exists. – S. Bell Jul 01 '18 at 11:15