Foreverforeign

she should confirm that with the employers immigration Lawyers, they will know.

There is cap and non cap so yes some are subject to the lottery.

correct, Universities and related nonprofit entities, nonprofit research organizations and government research organizations are cap exempt. OP if the employer is any of those my above comment might not apply 

H1b is dual intent so a couple of options
 
Go back for the immigrant interview
 
File to adjust status in country
 
Just gives you another option.

With a marriage in June-September 2021 and a target date of May 2022 to immigrate, you may not have any choice but to interview in her home country.
 
It takes 12-18 months to process a CR-1 spousal visa.  She can only interview where she has legal residency.
 
Recognition of muslim/non-muslim marriages in the Maldives is irrelevant.  As long as the marriage was legal where it was entered into, then it's legal for US immigration.
 
Upon entering the US with a CR-1 spousal visa, she automatically becomes a green card holder and is authorized to work immediately.  If you go the K-1 fiancee route, there would be 6-8 months of waiting inside the US for work authorization after applying for it.

A work visa would require a US employer to apply for a visa on her behalf.  A student visa is a non-immigrant visa requiring her to show a real course of study for a degree, how it would help her career in her home country, and a foreign home she intends to return to after getting her degree.  Nothing you have disclosed indicates she would qualify for asylum.
 
The CR-1 route is the appropriate route for the two of you.  Unfortunately, it will take longer than the timeline you want.  
 
 

If you want to get married CR1 is the obvious way to go, the other paths you mention are uncertain and shaky. If she is legally resident in Singapore (such as on a student visa) she can interview there. An immigrant visa is usually valid for a little under 6 months. My suggestion would be to get the ball rolling as soon as you can - get married as soon as possible, file an i130 for her, to try get her to an interview there before she finishes her studies.  Then she has up to 6 months to use the visa if she gets it before she’s finished. That’s a big IF right now. The whole process is likely to take somewhat over a year from when you file, hence the suggestion to get it all started as soon as you can. If things end up going unexpectedly fast there are ways to slow it down but you can’t usually speed it up. From what you’ve said it seems imperative she gets the visa before she finishes her residence period there.