Exit Ops Advice Needed: Project Controller in Big 4 or Business Analyst in mid-tier?

So, I got recruited into Deloitte Consulting last year into what I thought was FO.

Ended up being a BO support role of engagements as a Project Financial Controller looking at WIP and billing etc.

I think I was quite naive because I kept going to client site and thought I could make it to FO easy. Turns out, when I approached partners to get a FO role, almost all said that I could not enter their practice given my project control skills, except for Operations Consulting. And that too, they want me to come in as a Grad/Analyst, when I graduated like 3.5 years ago.

I am now stuck. I have been starting to look for exit ops because I realised that the only role that would take me easy and give me a promotion is a BO/MO project controller-type of roles. I am now a senior project controller, but I see no future in this. Am I right to think that? Are there good exit ops for people in support roles?

Due to the toxic culture in the previous controller team, I took the senior project controller role in Risk Advisory 6 months ago. Is there any future to staying in this part of the business to get a client-facing role?

I am close to getting a BA role at a mid-tier IT firm. Should I take that instead? Would that be considered more client-facing, that I can use this and get back into the firm as a senior con/analyst?

I believe the project controller skills are transferable (eg stakeholder management, creating finc data models etc).

I'd appreciate any advice on this! Thanks!

PS: I don't want to do an MBA. Looking for exit ops advice only