the tool must:
1) Test the page/component load/render time.
2) Be usable on multiple devices/browsers.
3) Show results with recommendations per-device/browser
Here is a presentation on "mobile web high performance".
Also, check out this question: Tools to simulate mobile devices on a desktop to test websites
The following tools may not meet all your requirements but you can check them out -
For some general recommendations, check the slides of the Mobile Web High Performance presentation at the Velocity 2010 conference