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When you unplug the router's LAN interface, wouldn't that also likely stop the router for doing much routing and/or stop most traffic transiting the WAN link? If so, it's reasonable pings to the external WAN interface would improve.
What's the load across the WAN link when there's high ping responses?
Also, remember, Cisco network devices respond to pings, to themselves, as a low priority item. I.e. poor ping responses from a router interface might not be indicative of any real issue, other than the router was busy doing something else.
In other words, why do you think LAN broadcasts are the cause of the issue?
Broadcasts are also generally necessary for correct network operations, so precluding them, or even limiting them, can cause other issues. Some switches do support broadcast flood bandwidth limits, but that's not a panache solution.
BTW, I'm unsure netflow will show broadcast "flows". If not, RMON type stats from hosts would show a breakdown of broadcasts being transmitted per host. (NB: not all hosts will record such stats.) Also if not, if you can packet capture the LAN, you'll see the broadcast packets. (NB: some later IOS images can do packet captures.)
