I need help and advice!

I currently work as an consultant at a large corporation. Came onboard for 1-2 years to help rebuild one of their platforms. From the beginning the mindset was that the finished product should not be developed based on anything else than customer testimonials and interviews regarding functionality and design. However, they’re building their platform developed and distributed by this other company. Basically they bought a system that is incomplete regarding to being compliant to the specifications brought to them when they decided which system to go with. Now we’re trying to build around all the issue this platform is causing us. The code base for the system is like something a monkey did with their feet. Nothing makes sense and it’s layers on top of layers of 10 year old code. I f-ing hate it. I don’t know what to do. We have some many technical limitation that it’s impossible to create the vision they had from the start.
I’ve been thinking about talking to the highest chief in the department as he has been pissed earlier about project managers not escalating issue to him earlier. But I don’t want to step on anyones toes. Should I leave the project? Should I talk to the chief? What do I do? I’m miserable🤯