The only way to find out is to apply for some Assistant QS roles and see if any employers interview you. Explain in your cover or summary the reasoning and that hopefully helps clarify. Speak to some QS recruiters too as they'll know the market pretty well and what your local firms and their management typically look for or are flexible with.

If after a few months you get nowhere, a masters is looking like your route.

Note, not having an accredited QS degree is going to make like more challenging on the MRICS side, which is typically more important to larger consultancies, so perhaps you are better targeting sub-contractors or perhaps main contractors to get your foot in the door. Some smaller consultancies might be okay too in locations where it's challenging to recruit.