1) First, I would recommend using more stringent criteria, especially if you are getting around 1500 gene sets. For example, just use FDR < 0.05 or FDR < 0.01.

2) Once you have confidently identified gene lists, I would great them in a discrete fashion (so, FDR = 0.01 is really no different than FDR = 0.0001)

3) You could use a table to list the most commonly represented genes. For example, 2 columns, 8 rows, where each row provides the count of common signatures. Hopefully, the list of signatures common to 7 or 8 models (or maybe even 5 or 6 models) is small enough that you could list every single signature. If you have only 3-4 most robust signatures, you could make a heatmap using the genes in the signature (if possible/reasonable, maybe you could combine all your datasets; it would be great is the corresponding groups in each of the relevant models clustered together)

4) You can visualize up to 5 gene signatures in Venn Diagram. If there is any way to prioritize among your gene models, then this could be an option.