Squeezy sequence, sideways sedimentation
JavaScript (ES8), 186 bytes
A direct transformation of the input.

s=&gt;(g=s=&gt;s.join``)([...b=g((a=s.split(n=Math.max(...s)))[S='slice'](0,(k=a[L='length'])/2))+(m=a[k&gt;&gt;1])[S](0,k&amp;1&amp;&amp;m[L]/2)].sort())+''.padEnd(k-1,n)+g([...g(a)[S](b[L])].sort((a,b)=&gt;b-a))

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