Terminal window as its own app
@mankoff got me on the right path. Here's what I had to do in order to get what I want:


Copy Terminal.app to a new file (ex: MyTerminal.app)
Change the icon of the app by:

Copy an icon image to the clipboard from Preview 
Right-click (Command-click) on the app
Select "Get Info"
Click the app icon in the upper left corner
Pasting the new icon image from the clipboard

Right-click on the App and choose "Show Package Contents"
Change the following values in Contents/Info.plist:

"Bundle display name" -> "MyTerminal"
"Bundle identifier" -> a unique app-specific string. I chose "ca.softcraft.myterminal" as I own the domain "softcraft.ca"
Bundle name -> "MyTerminal"
Document Types -> Delete
URL Types -> Delete
Application has localized display name -> uncheck
Exported Type UTIs -> Delete

I deleted a bunch of the localization settings (Contents/Resources/*.lproj) as they're not necessary for me; I just need English
In Contents/Resources/English/InfoPlist.strings, I deleted the "CFBundleName" and "CFBundleDisplayName" override settings
In Contents/Resources/Initial Settings, I deleted all but one of the *.terminal files.

I'm using a custom terminal setting, but there's no reason you couldn't use Basic
In Contents/Resources/Initial Settings/settings.plist, I made sure my "Default Settings" value was set to the name of my .terminal file

I set the values in the .terminal file to match what I wanted on open

This is just a .plist file with a different extension; you can use Property List Editor to modify it
You can also set these using Terminal itself and then export them
I mainly changed "CommandString" to be what I want launched when I run the new "app".



This works excellently. The new "Terminal" apps are independent of each other and of the main Terminal. I can spin off new ones fairly quickly now.

I also did this with Firefox to create a site-specific browser for my development website. (I had tried Mozilla Prism but found it too limiting).