I think it would be more beneficial to remove the ForgeMaster node from the Forge Strike tree and replace it to allow Forged Weapons to use Rive and benefit from its tree. Rive is used as a downtime melee attack while you regenerate mana from using Forge Strike, which is good but Rives Bound Weapon node becomes worthless. With any number of Forged Weapons around, you will not do enough damage with Rive in a quick enough time to proc Bound Weapons. If Forged Weapons could use Rive, they would be able to proc Bound Weapons to assist with uptime, and give them more versatility as a build. Of course the damage scaling of Rive could be altered to adjust for the minion usage, so I think quality of life and versatility of the change would be beneficial for Forged Weapon focused builds.
Yes, currently the forged weapons summoned by Rive have bad synergy with those from Forge Strike, and even the whole minion based Forge Guard spec.
Forged weapons summoned by Rive should at least get the duration bonus from Forge Strike, and still, resorting to killing blow makes them not pop that often