have you considered pursuing higher studies, either masters or phd, as an international student in canada first? tuition fees arent that much more expensive in certain universities, even highly ranked one, as compared to doing grad studies in NUS/NTU/SMU. for example, university of alberta and mcgill university charges international students less than $10k per year even for international students. with a canadian degree, it'll put you in good stead for a higher paying job in canada and will also allow you to qualify for CEC.
right now, FSW aren't running draws, and even when it resumes, I expect cut off scores to be very high, way higher than what an applicant with just a bachelor's degree can achieve. and even if you do eventually obtain PR via FSW, as you said, finding a job without canadian experience can be very difficult if you're not particularly skilled.
if you want to continue working in O&G, you can consider moving to alberta, either edmonton or calgary. that's where most of the O&G activities are. and your bf doesnt necessarily have to find a job in the same city if he's able to secure a job with remote work arrangements, although those will be hard to come by, especially without canadian work experience.
I recently moved to edmonton to do my masters in engineering and it took my wife a month to find a job, although it's not a job that she absolutely wants. she's still constantly applying to the jobs she wants, with the hope that having a job now will provide her with an added advantage. linkedin, indeed and monster.ca are good portals where a lot of professional jobs are posted. facebook marketplace is more for temp jobs.
all in all, although our income is lower than in sg now, i think we're happier because its less crowded here, groceries are cheaper, there are nice national parks within a short drive away and the weather's awesome (for now)
