Recently qualified ACA in Restructuring @ boutique (previously big4) looking for exit ops

Hi all, first post on here but hopeful there is someone able to advise!

I am a recently qualified ACA consultant working in boutique restructuring firm (previously big4) looking at potential exit ops.

I’ve had significant experience on trading administrations but limited exposure to advisory work despite nearly 3 years employment. My peers/mentor tell me this was their experience at this firm and I will be staffed on more interesting projects now that I am qualified, but it has been incredibly frustrating as I was sold on the variety of project work.

I now find myself wanting a new challenge but feel somewhat under prepared given my limited project work. My goal would be strategy consulting but feel that my lack of academic pedigree (US non target but full ride academic scholarship so made financial sense at the time) limits me to entry level. This I don’t mind as comp is only £45k+ c5k bonus at current firm (regional office).

My question is: if I remain at current firm I should have more exposure to advisory work over the next 6-12 months and would feel more comfortable applying as experienced hire (where I hope my non target school is less critical), but would I have a better chance applying at entry level?

Thanks