Three choices. I've been there and done that (for 11 years) but it was many years ago. First question is does your employer have an office in Singapore. If they do, it makes it easy for you. (My former company, Oceaneering Int'l has an office as well as a yard here). As, like yourself, the employees are multinational in nature, O.I. had rented a semi-detached house and used it as a guest house for their offshore staff who wanted to stay there during their off time. So, if they do have a presence in Singapore, have them rent the
condo in the company name and you can stay there during your month off. If you are from a western country with an automatic 90 day visa you should be in good shape if you are here only 28 days at a time (allowing one or two days travel time depending on where the rig is drilling). I only did that for one year but then (second choice) got married to a local girl and lived with her after that, but still on a normal 30 days SVP (this was before the 90 day visas for US passport holders). (third choice) As mentioned, stay in a
Serviced Apartment (considerably more expensive but some down around the $3500/mo level).
Legally, these are the only options available if you don't have any type of residency here. Getting caught out renting something illegally can get both you and the landlord in trouble. LL may pay a fine, you may be banned from Singapore. Are you willing to gamble?