You can actually hack the deployment process on BT a little bit further than this, if you want to omit the versioning, depending on your access to the actual BT box. (Convince your sysadmin)
If you only have access to the deployment console, stop your dependent applications, remove their reference to the application you want to upgrade, and then deploy over the top, re-add your references and restart the dependent applications. You don't actually have to reinstall.This method is tedious and sucks but it will work. We do this because we have too much in our BT installs to further clutter them with multiple versions of the same app
Here is the hack. You'll need either access to the server (which I know you said you don't have) or the ability to install a service which can receive a dll and preform the below function for you. (I'm thinking you might convince someone to let you set this up) DISCLAIMER, this is not a supported solution and I claim no responsibilty blah blah blah
We do this all the time as we have WAY too many applications to do the first solution. You can slam your newly compiled DLL into the GAC. This NOT recommended by MSFT etc. but we use it in production on servers that have approx. 4000 dlls in the GAC and 1200 BT applications. You'll need to make sure that your metadata is identical i.e. you have the same version, key token etc. and you'll want to have some way of tracking your dlls outside the versioning system (we build a custom deployment infrastructure to do this). Finally once you have pushed your dlls into the GAC you'll need to restart your biztalk services. Make sure you don't have any suspended instances referencing the app you want to redeploy because they will prevent biztalk from pulling a new reference from the GAC when it restarts.
Finally it is important to note that this method will NOT work if your changes require changes in the MessageBox subscrition (things like changes in receive shape filters, correlations etc.) You will also be giving up some functionality in the orchestration debugger if you use this method to change the structure of orchs. The graphic will display the structure of the orchestration when last properly installed but your event list will be correct for the newest version. Finally, if you are replacing schema dlls you want to make doubly sure that you restart services as BT will cache schemas indefinitely.