If all you have is a EE degree, than you won't be able to deviate much from eng. The max is you can go into other industries as SWE, which as you mentioned is not what u are good at.

If you really want to go in other roles, you gotta decide on it and learn about it via Coursera or something. Then you can take a few routes:
1. Take an internship in that area and try to convert.
2. Go for some MA/rotational program if you can (it's competitive)
3. do master's (perhaps MBA).

But it all boils down to the fact that the employers want to see that you are really interested and you know what u are getting into. The big question for them will be if you did EE and don't like it, what if they take you for this role and u quit after 2-3 months. You gotta have a good reason to convince them and some background to show for it.

I am a ME grad, who got into a strategy role (M&A). Did it through the MA program. But at the same time I had an interest in finance, so did learn a lot about it myself (books, , Coursera courses) and I would say I have strong basic knowledge of it. That's enough to get me into an interview, but then I have to really sell myself. One this you should make is that your background gets you a lot of skills that business or other grads lack, especially logical and analytical thinking, highlight it. Say your background brings a different perspective to the table which is important for the diversity of opinion.