No experience of this HU, but I use the same database on my Zenec and RNS510.
With the Zenec there is a menu in Warning's where I can 'alert only when speeding', would be surprised if the Kenwood doesn't have a similar option.
As for multiple warnings, maybe there is an option to 'alert only on route', or turn off repeat warnings for the same.
Have a play in the menu's see what's available.