Is there any way to get around a high waste outlet pipe?
I can think of three solutions.
Raise the countertop
Increasing the height of the countertop, could give you enough height to install a proper drain.  Though I'm guessing you won't want to redo the cabinets and countertops.
Modify the plumbing
Lowering the inlet in the wall would give you enough height for a proper drain, and is likely the most common solution.  It looks like that may not be an option i your case, as it looks like that might be a concrete wall.
Install a basin pump
Drain the sinks into a basin, and then lift the waste water with a pump.  SANIVITE® makes the SANIVITE®, which is designed for this type of install. I'm sure other companies offer similar products, so shop around to find one to meet your needs.
With this type of setup, you'll need a power source, and enough space to fit the basin.

Whatever you decide, the current plumbing definitely needs to go.  All the pipe that's below the throat of the wall inlet, will be full of water. That means the trap seal is likely too deep, which will lead to frequent clogging and slow draining.


I do not recommend nor endorse the use of any product mentioned here, all products are mentioned for example purposes only.