I too read the thread hoosierbanana posted and I got to thinking this may be for me. I agree with her that timing is important. As well I would say that the pumpkin stem is huge compared to the watermelon, so a light touch is needed when inserting the cuts together.
I have tried watermelon before, and I have a greenhouse that is warm from mid March till the end of Nov. and still I could not get watermelon fruit. I am not sure if it is the soil, the temps. or the amount of transplanting needed for potting up, but my grafted, I have 6, have surpassed the 6 non grafted by a mile.
I did the approach graft as the video suggested at the two leaf stage, I used teflon tape instead of tinfoil because I found that if the tinfoil was left on longer then the stem, as it grew, was actually cut by the edge. I cut the pumpkin leaves off at the prescribed time of 5 days, and the roots at varying times. I did 7, 10, 12, and 14 days, the 12 and 14 day ones seemed to have a better take. Many watermelon and pumpkin seedlings gave unselfishly of their lives to my blundering attempts while trying to learn what worked
For sure, if you can already grow watermelon or other melons, there is no need for all this fuss. I don't have squash bugs, and as for powdery mildew no problems yet.
All in all this was actually quite a fun project, grafting was finickity as the stems are incredibly small and tender and slicing clean thru happened a lot. But it is something to consider for those of us in colder zones. I will repeat it next year, one year of 12 plants is not large enough to say that this would always work.