Can お[邪魔]{じゃま}します be used in cases of long-term stay?


So I need to write an email for an assignment where I am an exchange student
who is going to Japan and staying at someone's house for a period of time.

I want to begin with "thank you very much for having me" which would normally
be お邪魔します as watching Japanese shows with subtitles have taught me. But I feel
like お邪魔します feels more like a short-time thing like "sorry for the (temporary)
intrusion" as opposed to something along the lines of what I want to say.

What would be more correct in the context that I am writing in?




I think お邪魔します is used in cases of short-term stay as you said.

I think お世話になります is natural in cases of long-term stay.




I think お邪魔します is used in cases of short-term stay as you said.

I think お世話になります is natural in cases of long-term stay.

