My draft, quick-shot proposal (change however you want):

Every gossip wire level message contains branching factor BF
There is a variable in every node, current branching factor CBF
There is a configurable initial branching factor IBF
There is a configurable dampening factor 0.0 < DF < 1.0
There is a configurable minimum branching factor MBF >= 1

On events that change my current version:
- If I bump my version (fork) -> CBF := IBF
- If I merge an external gossip G -> CBF := G.BF (or should CBF := max(CBF, G.BF) ?)
- if no change -> CBF = MBF

On a gossip timer tick
- Send CBF number of gossip messages, each having G.BF = max(CBF * DF, MBF)
- Set CBF := MBF

There are some cases to be considered when multiple changes are disseminated at the same time, but I think it should work.