I’ll answer my own question here, as I tracked down the problem.
The issue is with how the Hugo passes Asciidoc page content straight to an external parser, rather than pre-porcessing it first. So we need to tell the external Asciidoc parser to passthrough the Hugo shortcodes unmodified. From the Asciidoc Syntax Guide
++++
<p>
Content in a passthrough block is passed to the output unprocessed.
That means you can include raw HTML, like this embedded Gist:
</p>
<script src="https://gist.github.com/mojavelinux/5333524.js">
</script>
++++
So, in the case of Hugo shortcodes, it was simply a case of adding those ++++ passthrough fence-blocks to the shortcode. So that:
{{ "<!-- begin image shortcode //-->" | safeHTML }}
<figure {{ with .Get "class" }}class="{{.}}"{{ end }}>{{ with .Get "link"}}<a href="{{.}}">{{ end }}<img src="{{ .Get "src" }}" {{ if or (.Get "alt") (.Get "caption") }}alt="{{ with .Get "alt"}}{{.}}{{else}}{{ .Get "caption" }}{{ end }}"{{ end }} />{{ if .Get "link"}}</a>{{ end }}{{ if or (or (.Get "title") (.Get "caption")) (.Get "attr")}}<figcaption>{{ if isset .Params "title" }}{{ .Get "title" }}{{ end }}{{ if or (.Get "caption") (.Get "attr")}}{{ .Get "caption" }}{{ with .Get "attrlink"}}<a href="{{.}}"> {{ end }}{{ .Get "attr" }}{{ if .Get "attrlink"}}</a> {{ end }}{{ end }}
</figcaption>{{ end }}</figure>
{{ "<!-- end image shortcode //-->" | safeHTML }}
Becomes:
++++
{{ "<!-- begin image shortcode //-->" | safeHTML }}
<figure {{ with .Get "class" }}class="{{.}}"{{ end }}>{{ with .Get "link"}}<a href="{{.}}">{{ end }}<img src="{{ .Get "src" }}" {{ if or (.Get "alt") (.Get "caption") }}alt="{{ with .Get "alt"}}{{.}}{{else}}{{ .Get "caption" }}{{ end }}"{{ end }} />{{ if .Get "link"}}</a>{{ end }}{{ if or (or (.Get "title") (.Get "caption")) (.Get "attr")}}<figcaption>{{ if isset .Params "title" }}{{ .Get "title" }}{{ end }}{{ if or (.Get "caption") (.Get "attr")}}{{ .Get "caption" }}{{ with .Get "attrlink"}}<a href="{{.}}"> {{ end }}{{ .Get "attr" }}{{ if .Get "attrlink"}}</a> {{ end }}{{ end }}
</figcaption>{{ end }}</figure>
{{ "<!-- end image shortcode //-->" | safeHTML }}
++++
Then they work properly.
I thought I was away there. But, unfortunately I’ve now run into another [seemingly insurmountable] problem, which will merit its own post!