My first thought is to check the egg and yolk weights, check that the pumpkin was sufficiently evaporated on the stove prior to mixing the custard, and check the final temp and that it’s chilled long enough. Sounds like you probably did take care of those details, is that right?
Rose’s goal for custard-based cakes (cheesecake, oblivion) is to create the softest, creamiest texture that will still be sliceable. You may prefer a firmer cheesecake. One way to firm it up might be to replace some of the cream with a smaller amount of butter, so that you retain the butterfat while reducing the water content. For instance, if you’re using 36% butterfat cream and the recipe calls for 2 cups, try it with 1.5 cups of cream. The missing half cup of cream would have about 42g of butterfat. Replace it with 52g of butter, which has the same amount of butterfat as the missing cream. And then you might need to trim the sugar back by a few grams to keep from making it sweeter by leaving out some of the water. You could also cook the pumpkin longer to evaporate more of the water, though you’d have to be careful not to brown it.
Please report back if you try it again in a firmer version