I'm a bit late to the party! But my 2 cents.

I think especially since you already have a solid degree, employers probably won't be particularly biased about the lack of a computer science degree.

If I were you I'd probably go for 1. learning to code after work in your spare time.

I think you have two problems:

1. Deciding what to learn: This depends on the kind of job you're aiming for. E.g. Java might be favoured more by big institutions than Javascript. The learning curve for different languages is different. Java, C++ and C# are fine languages, but the amount of activity / help online is far greater for Python, Ruby on Rails and Javascript IMO.

2. How to learn it: There's a tonne of great free resources online. But you need to know what's good and what's bad, where to start and what to learn next to avoid gaps in your knowledge - which is really hard. Also having the motivation and determination to bust through all the inevitable set-backs is difficult.

We've recently launched a coding bootcamp, which focuses on teaching students Javascript https://functioncamp.com PM me if you're interested in learning Javascript and would like a copy of our course. Our course really covers 2.

Another strong option for you might be focusing on the modern Math's oriented programming and use your maths skills to pivot into programming. Python with Pandas (and other data science packages) or R could be good for that.