I direct sowed birdhouse gourd seeds very late this year,maybe June?,and 5 plants probably had 15 mature gourds with a few more immature ones.The vines were probably a 20 foot diameter.Hope this helped some.
Gene

Hi. It sounds to me like 15 seeds will be fine for your fence. Some of the vines will probably crawl over each other, but I have found that they're usually not very fussy about that. For most gourds and squash, I usually start seeds indoors about 4 weeks before transplanting outside.