Ambroos is definitely a conceivable nickname for
Ambrosius, but
Broos would probably be even more so - the Limburgish people generally like short, one-syllable nicknames, and as such,
Broos is more likely to occur than
Ambroos.
As for
Adrianus,
Arjan is more Dutch than it is Limburgish. Nicknames found for
Adriaan and
Adrianus in Limburg include the following:
Aad
AdAdje
Adri (or Adrie)
Driaan
Jaanes
JanJanusJäôn (really difficult pronunciation for a foreigner, it somewhat resembles the English word 'yawn')
Jaon
I have seen Aad and
Ad the most often, but for a prince, I think Adri would fit best - Adri seems a bit more 'posh', if you will, while Aad and
Ad are more 'cheap' (i.e. more for commoners).
In case you're wondering: yes, I am from Limburg (in The Netherlands), so I would say that I do know what I am talking about here. :)
Anyway, I hope this helped you somewhat. :)