This is an easier job than people make it out to be.
I used this fluid extractor with the included small flexible hose:
Name on Amazon: Thorstone 200cc Automotive Fluid Extractor Pump, Manual Oil Change Syringe with 50cm Rubber Hose & 2pcs 22cm PVC Suction Tubes
No need to remove the brace entirely, just remove the e10 bolts. Then you can use a 6 inch extension to access the fill hole behind the brace.
With the extractor, new plug, and fluid this is a sub $75 - 1.5 hour job.
If you haven't changed your transfer case fluid yet, do it now.