Irrational, I read your description too fast and missed what Moses just pointed out, namely that your Reilly's stock has a notched horn buttplate. Personally, I would be reluctant to mess with these nice original features by doing a stock extension, which would necessarily eliminate the notched horn buttplate. I would be inclined to use a boot, as others have suggested. I think you may have a good selection of boots in the UK. The nicest ones I have seen here recently are made by Gary Fatherree at Accu-Riser. Their website is
http://accu-riser.com