這句可否改寫成這樣？

I have got until the end of the month to pay the money back.
中文是: 我必須在月底前還錢。

No, you cannot change the structure of the sentence.

"until the end of the month" is an adverbial specifying the time limit of doing a purpose "to pay the money back" (an adverbial of purpose).

There is a more common way of saying it:
I have been given until the end of the month to pay the money back.
我被給與期限，在月底前把錢還回。

2012-08-01 21:26:50 補充：
I have got to pay the money back by the end of the month.
= I have to pay the money back...
中文是: 我必須在月底前還錢。

I think it should be written as:
I have to pay the money back by the end of the month.
我 要 在 月 尾 還 清 款項 - this is the Chinese explanation.

From my point of view, the original sentence cannot be changed into this way, otherwise the action 'I have got to pay the money back' will be done before the end of the month as the meaning.