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The only techniques i know are those in the title.

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    $\begingroup$ Balancing may not be the correct term, balancing refers to AVL, Red Black, Splay tree like structures. You seem to be looking at decomposition. What kind of decomposition are u interested in. Look for Topology Trees, Top Trees, Euler Tour Trees, Sleator Tarjan Trees (uses heavy light decomposition) for several similar decomposition. $\endgroup$ – sbzk Oct 19 '17 at 7:26
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The paper "Algorithmic Meta Theorems for Circuit Classes of Constant and Logarithmic Depth" (Elberfeld, Jacobi, Tantau) gives a nice balanced tree decomposition based on tree contraction in $TC^0$:

https://eccc.weizmann.ac.il/report/2011/128/

Another nice $TC^0$-decomposition is based on so-called TSLPs in the paper "A Universal Tree Balancing Theorem" (Ganardi, Lohrey):

https://arxiv.org/pdf/1704.08705.pdf

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