Is there any way of stopping the "No more attempts" message box from appearing?

I prefer to have an 'incorrect answer' pop up with detailed feedback.

If you want to limit the number of attempts at question you can still use the no more attempts pop up to show whatever text you need to.
Just change the properties for the queston. In the feedback tab change the text used in the no more attempts feedback section, that's the tet in the text box. The detail text message can be added by clicking on the TE (text Editor) button and adding whatever you need. You still get the indicator that you've exceeded the number but the text is your choice.
This wil be the simplest way to do this

OR .....
If you drop a question object onto the page and populate it then you can assign actions to it rather than use the pre scripted events. There are actions avialable for the events you want to capture.
So if you made a fully detailed response in a pop up then hide it you could have an action for on failure reveal the pop up.
This might be more what you really want to happen.

I just had a play with the actions and it works fine.
So just add the question object, populate it with the answers and set any limits like number of approaches.
I threw everything at this and had an action for:
On display question
On change choice
On success
On failure
On timeout
On attempts limit
On skip question
Which really does cover whatever you need very flexibly!!