I'm sure you are aware of the different forms of (spoken) arabic, MSA being quite distinct from Gulf Arabic - and this itself breaking into two or more dialects within Oman. Oman would not perhaps be the first choice for learning arabic, although with your work centred on Qatar and Oman, and Oman a far nicer place - by a very large margin - than anywhere else in the Gulf, go for it! But probably best to find a structured course rather than try to polish what you already have through daily exchanges.

There's a specialised school known as CIL, and an American outfit as well as courses given by other language schools. I don't know if they teach colloquial Omani or MSA: but probably they do both. The British Council doesn't run arabic classes, but I think they would be an excellent source of information and advice:

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