UPDATE TO ANSWER

Ok after a little play with sandboxing which I have never used before: I used the option :

However, for applications that specifically provide scripting access groups, you can send appropriate Apple events to those apps if your app includes a scripting targets entitlement.

For other applications, by using a temporary exception entitlement, you can enable the sending of Apple events to a list of specific apps that you specify, as described in Entitlement Key Reference.

So in the Entitlements file.

You need to add the Entitlement:

com.apple.security.temporary-exception.apple-events

Set it as an Array

Then add two items to it.

com.apple.systempreferences

com.apple.systemevents

These items should be strings

Save the file.

This is All I have done and there are no other entitlements added

On my tests the System prefs opened and the Proxies tab was selected.

This also shows any App you that even if you tell one app to tell another app/process ..do something. Both apps must be in the list

A slight change to your setup should fix your issue:

By doing this I notice that in your edit you show you have added:

com.apple.preferences.

So you just need to change it to the correct id which is com.apple.systempreferences

Original part of Answer:

If you read the AboutAppSandbox link I provided you in the comments. Which I suggested as I assumed your app was sandboxed already. You should have seen:

Use of accessibility APIs in assistive apps With App Sandbox, you can and should enable your app for accessibility, as described in Accessibility Overview for OS X. However, you cannot sandbox an assistive app such as a screen reader, and you cannot sandbox an app that controls another app.

( I have literally just read this myself )

This implies with regards to accessibility APIs in assistive apps And sandoxing, you can do one or the other but not both.

There is however this bit also but you will need to investigate its implications

However, for applications that specifically provide scripting access groups, you can send appropriate Apple events to those apps if your app includes a scripting targets entitlement.

For other applications, by using a temporary exception entitlement, you can enable the sending of Apple events to a list of specific apps that you specify, as described in Entitlement Key Reference.

And reading further there is another possible approach

Finally, your app can use the subclasses of NSUserScriptTask class to run user-provided AppleScript scripts out of a special directory, NSApplicationScriptsDirectory (~/Library/Application Scripts/code-signing-identifier/). Although your app can read files within this directory, it cannot write files into this directory; the user must manually place scripts here. For details, see the documentation for NSUserScriptTask and WWDC 2012: Secure Automation Techniques in OS X.

The strategy you are using is not what I would want from an app. And I think using GUI like this leaves a lot of room for it to fail.Either because of element tree changes in the GUI or user interaction takes focus away from the intended target of the system events.

I think the better approach would be to inform the user to change the proxy their selves.