Paul, I am glad I could be of help.  :)

I agree with your summary overall, except in Suzy's case, she is expressing hope mixed with a larger does of DOUBT - not frustration or impatience and definitely not resignation.

Hope that was helpful.  :)

I want to give another example to highlight Matt's first paragraph (which I agree with).

"By using "if", it is possible it will happen and possible it won't happen. By using "when", we assume it will happen and some other event (in you sentence, being able to proceed to the final stage) will happen afterwards, but not before."

Let's say you have a comprehensive test that you must pass before you can get the job of your dreams.  You are allowed to take the test once every 6 months until you pass it.  There are no limitations on how many times you can take this test.

Your friend Suzy, says to you, "Paul, if you ever pass that test, I will take you out to an expensive dinner to celebrate."  Your uncle Erich has already said many times, "When you pass that test, I will give you my car so you can have transportation to your new job."

Which one believes that you WILL definitely pass the test (and get the new job)?   Which word in each sentence gives you that clue?

**In the US, using "if" is sometimes seen as "bad luck" (in instances like above).

<font color="#000000" face="Calibri" size="3">Matt,</font>

<font color="#000000" face="Calibri" size="3">You would have made an excellent English teacher for   a slow person like me. Thanks a lot for your efforts! By the way, in respect to the problems at hand the German and English language are quite similar. I am going to read your example sentences again and again until I can apply them automatically.</font>

<font color="#000000" face="Calibri" size="3">Kind regards,</font>

<font color="#000000" face="Calibri" size="3">Paul</font>

By using "if", it is possible it will happen and possible it won't happen. By using "when", we assume it will happen and some other event (in you sentence, being able to proceed to the final stage) will happen afterwards, but not before.

As for moving "only", that is fine in your sentence but sometimes can give a second possible meaning. It probably wouldn't be interpreted in the other way unless context made it clearer.

I'll try to give some examples:

We can go to the beach when you want. - I know you want to go and any time is OK.
We can go to the beach if you want. - I don't know if you want to go but if you do, it is OK with me. However, when is unknown.

I will try to reply when you message me. - I assume you will message me and will reply after you do. Probably soon after.
I will try to reply if you message me. - I don't know if you will message me but I will reply if you do. When is unknown.

You can speak only when I tell you to. - First I will tell you that you can speak, then you can.
You can only speak when I tell you to. - First I will tell you that you can speak, then you can, but maybe you can't do anything else.

He will walk only if I walk. - If I walk, maybe he will walk, but if I don't, he definitely won't walk.
He will only walk if I walk. - If I walk, he will walk but nothing else, e.g. stop running, or the same meaning as above.

The sentence is completely correct, and there is no need to be confused or to change anything,.

The issue is not about whether or not the Committee is convinced, but about the point at which it is convinced. First the Committee comes to its decision, then he can proceed to the final stage. In other words, he can't proceed until the Committee has decided. This is about timing and a sequence of events. It answers the question 'When can he proceed?'

'Only' has to go before whatever element of the sentence it is modifying or restricting. In this case, it goes immediatelybefore the clause 'when the Committee...'. He can proceed only when this has happened, and not before.

You could move the 'only', but strictly speaking this would change the meaning of the sentence. If you moved it to before 'proceed', it would modify 'proceed' .This would mean that proceeding was the only thing could do at this point i.e. he couldn't do anything else.  This is nitpicking, of course. In everyday conversation, you could certainly say 'He could only proceed..' and nobody would misunderstand you. But when it comes to formal and legal wording, the position of 'only' really matters.

And in this sentence, 'only' is in exactly the right place.