I think it could definitely be a fit. An in between option would perhaps be being a ME at a more strategic design firm like frog where the MEs are often time doing more high level thinking collaboratively with the design team. When the rubber hits the road you would still be deep in ME stuff, but a lot of times the engagements are more high level and front end. It is possible to eventually transition into an interaction designer in such a roll, or even a director. One of the ID directors at frog at the time (since left) had an ME background.
If you really want to go hardcore ID though, yes, going back to school is going to be the most reliable path. With an ME degree and work experience in a design firm you should be able to do the degrees in less than 3 years (the school will probably try to say 3-3.5, but realistically I would think 2.5 if you push on them). SFSU isn’t bad, and I think if you know what you want out of the experience you will be fine. Maybe you can even work part time as an ME at a firm during?