How to deal with low space and high current?
Here's a little tip for you:

The thickness of trace needed can be seen as a function of the length of the trace.  The longer the trace the greater the voltage drop, and thus the thicker the trace needs to be.

Online calculators all assume the trace will be a constant width the entire length.  This is not the case in your (and many other) situation.

So treat your layout as two traces.  One trace that is the length from the chip to the start of the wide portion, and a second that is the length of just the thicker portion of the trace.

Perform two calculations - one for each portion.  You'll find the shorter portion of the trace can generally be thinner than the rest.

Of course, if you go too thin then the heat dissipated could get too high, so it's a bit of a balancing act - try and keep the thin trace as short as possible.