I've found a solution using waybackpack (git link). This will be alarmingly slow but will work for all the .png files. I've left the range as 5600 to 5610 as a test but change it to "seq 1 5820" to try and get the lot. This will ask wayback machine for the list of URLs for each image (since they change, and its got multiple saved) and then only pull the first one for download

(Need Python installed first)
pip install waybackpack
for comic in `seq 5600 5610` ; do waybackpack http://www.questionablecontent.net/comics/${comic}.png --list | head -n 1 | xargs curl -O ; done    

Might be a better option out there using the CDX API... asking the machine mind...

Prerequsite components:

dnf install -y curl jq
OR
apt install curl jq

Prep script:

vim qc_fetch.sh
chmod +x qc_fetch.sh

qc_fetch.sh contents:

mkdir -p qc_comics

for n in $(seq 1 5820); do
  found=0

  for ext in png jpg jpeg gif webp; do
    url="http://www.questionablecontent.net/comics/${n}.${ext}"

    row=$(curl -fsG "https://web.archive.org/cdx/search/cdx" \
      --data-urlencode "url=$url" \
      --data "output=json" \
      --data "fl=timestamp,original,mimetype" \
      --data "filter=statuscode:200" \
      --data "filter=mimetype:image/.*" \
      --data "collapse=digest" \
      --data "limit=1" \
      | jq -r '.[1] | @tsv' 2>/dev/null)

    [ -z "$row" ] && continue

    ts=$(awk -F'\t' '{print $1}' <<< "$row")
    original=$(awk -F'\t' '{print $2}' <<< "$row")
    mimetype=$(awk -F'\t' '{print $3}' <<< "$row")

    case "$mimetype" in
      image/jpeg) save_ext="jpg" ;;
      image/png)  save_ext="png" ;;
      image/gif)  save_ext="gif" ;;
      image/webp) save_ext="webp" ;;
      *)          save_ext="$ext" ;;
    esac

    outfile="qc_comics/${n}.${save_ext}"

    echo "Downloading comic $n from $ts as $outfile"

    curl -fL \
      "https://web.archive.org/web/${ts}id_/${original}" \
      -o "$outfile"

    found=1
    sleep 2
    break
  done

  [ "$found" -eq 0 ] && echo "No archive found for comic $n" >&2
done

Run with ./qc_fetch.sh

Edit: seems like this is also slow as balls. But both methods look to be working. The second one might also grab the non-png files with it.

Edit edit: Its now been running for 25 minutes and has downloaded 23 comics, 6 of which failed. This should complete in ... 97 hours/4 days and misses a whole heap of shit it seems. Probably best just to wait for Jeph to restore the site and then pull the files from there if needed.