I like writing posts that end with "Here's my solution". This is not one of them. I'm just documenting this fight so that I can come back to it if I ever find a solution.
I opened up SharePoint Designer to create my new view. I selected "File: New: Page: List View Pages: Document Library View Page Wizard". I selected the picture library to which I wanted to add the new view, and named it "kenburns.aspx".
It starts to go wrong
Here is where the experience deviated from development. When I hit OK on this dialog, it went back to the designer and spun for a while. After a long timeout, it came back with the message "You do not have permission to do this operation." I checked my permissions and confirmed that, yes, I have full control of the entire site.
Going back and forth, I discovered that any change I make to the page causes this error. I can create pages, I just can't edit them afterward.
I started up Wireshark and inspected the traffic. I noticed that there were several duplicate ACKs followed by retries. So packets were getting dropped on the way back to the server. This is probably related to the VPN. I wanted to get this change up tonight, so I didn't have time to fight with the VPN.
So I got clever
I made small incremental changes to the page, but instead of saving it, I copied the contents into a local file, deleted the one I was working on, and then uploaded the copy. After each incremental change and upload, I verified with a browser that the change worked. Tedious, yes, but it worked around the problem.
At least it worked for a while. After a few iterations of this, I could no longer upload the file. Within SharePoint designer, I received the same "You do not have permission to do this operation" message as before. Based on the range of problems that I saw when Googling this phrase, I figured this is SharePoint Designer's way of throwing up it's hands. I even discovered that this error message is a hold over from FrontPage. It's been there a while.
I also tried uploading the file through Explorer. SharePoint does some WebDav magic that makes it possible to connect to a site using "My Network Places: Add Network Place." I navigated to the proper folder and dropped the local copy into it. After a long timeout, I was greeted with "Connection closed by remote server." This is more accurate based on what Wireshark was telling me, but no more helpful. I'm still back in VPN land.
Then I got desperate
I logged into the server via Remote Desktop, opened a command prompt, and executed "iisreset". No help. Then I restarted the box.
Let me pause right here and tell you that I knew at the time that this was a bad idea. I've felt that disconnected, sinking feeling many times before when the machine I'm working on is miles away, I have only a tenuous connection, and decide to let even that connection go. It's like being in a Spielberg movie when the background falls away while the main character is suspended mid-frame.
So I hit "Start: Shut down" (scary enough already) and "Restart". This being Windows Server 2003, I selected an excuse. The remote session was wrenched away from me. And then I waited. And waited.
(fall away and queue eerie violins)
The server still hasn't come back up. I've sent emails asking the next person to go to the office to restart the machine. I'll be in the office tomorrow afternoon, so you can bet I'm installing SharePoint Designer on the server!