Freshping is on to a good start.  The interface is nice.

Freshping needs 

1. Dependencies to prevent a flood of alerts if an edge router dies (I got sick of monitus promising this but never delivering).  
2. Maintenance windows (that cascade through the dependencies).
3. Automatically generate PDF uptime reports configurable across any time period for a range of devices.

Our staff don't want awakened at 3am for a minor website going down so there needs to be:-

1. Per device alert levels 
2. End user contact groups (e.g. on-call, daytime-only).
3. Configurable time windows    (24/7, working hours, daytime only, night time)

Currently using nodeping as it does most of the above but it's a bit "clunky" to use.

Also SMS and voice call alerts need to be built in.  I don't particularly want nor have time to muck around with 3rd party stuff like twilio.

Agreed on all these points, especially flood protection.