What's your App?
I don't know of any websites, but I can personally try it for you on a:
-Nexus 4
-Galaxy Nexus
-Galaxy S2X
-Galaxy S3
-Galaxy Note 2
-HTC Evo Design 4G
-Xperia Ion
-Sidekick
-Optimus One
-OG Kindle Fire (running CM9)
-Nexus 7
-BlackBerry Z10 (in case you're curious if it'll work for sideloading to that device)
I unfortunately have no Motorola devices anymore though, sorry.
Let me know if my stockpile of devices can be on use to you.
Keep in mind it's a dozen devices & I'm one person so I'll need strict test-cases to follow, I won't be able to provide "exploratory testing" for all devices - for a few I can manage. In other words I can check that your App launches on all devices & continue with a few simple checks you outline then do more detailed testing on a few choice devices.