All day today, I have been successfully accessing each and every site that I have tried to go to and not one disconnection. One thing is that I am using Linux to tether. That alone fixes a lot of issues. Secondly, Linux makes it very easy to change the MTU settings. I set it to 1300 and all sites, including my own, have loaded as fast as can be. I've also reached speeds on speedtest.net as fast as 27Mbps down and 9Mbps up. It seems that the LG Revolution has an issue with MTU when tethering, or using HotSpot.
I have the unlimited data plan, along with the unlimited hot-spot, and specifically asked the question when I added the hotspot feature that my usage was unlimited and she said there will be no restriction on your plan, whatsoever. As of now, I am at over 13gigs of total data according to MyVerizon app. So, the problems you are facing, may not be blocked websites, but websites that don't do well with MTU settings above 1300. I had a similar issue with a T1 line at a previous job, where the MTU settings were causing a stall on certain websites.
My suggestion is, before blaming Verizon network, which is by far the best available for wireless phones, try changing local settings. I had success with hot-spot, garden tether, adb usb tether, and usb tether, just by changing the MTU settings. Now the next phase is changing such settings in Windows, which is a network nightmare in it's own since MS doesn't like to follow standards and breaks things, such as ever since the SP1 update for Win7, I've had numerous Network issues, even on wifi routers that have worked flawlessly in the past and work flawlessly in Linux (on the same computer/laptop).
Information gathering is always of help to resolve similar issues between like users. I hope this post has some useful information to help others resolve issues like I've described and are like those in this thread.