Ah, right, I see your problem. I thought the EYFHS had got the headstones transcribed while they were still all ranged round the perimeter walls after the cemetery itself had been cleared and grassed. I would imagine then, that the answer is that HUll City Council took them away, broke them up, and used them for hardcore somewhere! The whole area was levelled in the early 1970s and everyone moved out to Bransholme (we'd already gone, five years before) so there wouldn't have been any local residents around to object, and in 1970, family history research was still in its infancy, I remember when I joined the EYFHS in 1976 I was only member number 269, at that time.
One thought that might be worth pursuing - I was recently ploughing through the wartime Hull Daily Mails for research for a forthcoming book, and I happened to see a sort of statutory notice that the council had obviously had to put in the paper because they were proposing to demolish and clear the old Methodist Church in Cogan Street, which had previously been a Synagogue, going way back when... anyway, they were advertising in this great long rigmarole because the site contained human remains and they were proposing to remove everything, and the advert also contained a list of all of the people mentioned on all the remaining memorials. I wonder if this was a staututory thing, and if so, whether the council were obliged to put one in the paper for the Drypool and Southcoates Cemetery. Might be worth a trawl.
But yes, generally, Hull City Council's attitude to historical artefacts in the 1970s makes the Philistines look like paragons of culture. The Crowle Street and Empringham Street "shrines" (street memorials to the local dead of the first world war) also disappeared around the time of the demolition, and nobody knows what happened to them, either. Fortunately, in WWI the HDM had already published lists of the names inscribed on them, but even so...
At least these days all the GRO indexes are online with people like Ancestry and Findmypast, so we no longer have to go schlepping down to Alexandra House to heave those huge index books around!