Solarwinds Engineer Toolset has Enhanced Ping - it does all of this.
You can use the ping tool in the Engineer's Toolset to to a continuous ping with timestamps, but you will have to export to HTML/CSV/TEXT manually (couple of mouse clicks...)
The classic Ping will allow you to do this as well if you are only interested in pinging one device at a time.
Start Menu\SolarWinds Engineer's Toolset\Classic Tools\Ping & Diagnostic\Ping
Start Menu\SolarWinds Engineer's Toolset\Classic Tools\Ping & Diagnostic\Enhanced Ping