It seems that the new FW2.35 has implemented some kind of Game ID verification for downloads, because it returns an error 80023300 when you download a different with a different game ID.
After a few tests I found that the Proxy works if you replace the *real* link and download the game from the PSN store. So now you're forced to install from the PSN store, instead of use Folding@Home or the PLAYSTATION®Home icon. This new method is less convenient than before, but at least the proxy still works, just that in a different and more difficult way. So the good news is that we can continue using the PC's download accelerator to download large demos and don't have to redownload the uninstalled demos again.
Example:
0-I assume that you have your PS3 connection configured to use the proxy.
1-Run the PS3.Proxy.Server.GUI, tick the PS3 option and Start the proxy.
2-Enter to the USA PSN Store, and browse until you find the demo that you want to install and start the download
3-Cancel the download immediately you see the download bar
4-Open the PS3.Proxy.Server.GUI and go to the Logs tab
5-Right click to copy the URL of the game
6-Go to the Replace Files tab, press the Add button
7-Paste the link you copied in the step 5 in the left field
8-Select the small button in the right field and browse for the downloaded PKG file
9-Select to download the demo again on the PSN link
10-Wait until it installs the demo.
Unlike the previous method using Folding@Home download icon, now you can use the background download.
I haven't tried sithvegeta's method, but it sounds interesting for demos not longer available in the PSN.