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Need for Computer Science conversion MSc if already software engineer?

Hello, I was wondering if anyone could advise me on whether it would be worth the time to obtain a computer science conversion MSc if I have already been employed for the past 5 years as a software engineer and have two years of ML research experience.

My motivation for the CS conversion application is that my undergraduate degree was in neuroscience and complex systems, which was somewhat computational but not formally a computer science degree, which seems to disqualify me for applying to most specialized master's programmes in Artificial Intelligence or Software Engineering. My current plan is to get a CS MSc conversion degree, and then a second master's in Artificial Intelligence/ML/SW engineering.

My motivation to get a master's in the above in the first place is to expand my options in being selected to participate in machine learning projects at work and in future employment - the country I am from is very big on formal qualifications so ML engineer positions tend to be reserved for those with postgraduate education. Also, my research experience was in reinforcement learning, whereas I wish to proceed into the direction of computer vision instead.

Would my plan as is be a waste of time and should I just apply for the more specialized programmes in the first place, or is it more or less impossible without obtaining a conversion CS master's first given my experience?

Sorry for the long first post and I thank you for your help, in advance.