Relaxation possibilities of the lower bound worst case sorting algorithms without quantum computation
Fist of all the $\Omega(n \log n)$ lower bound only applies to comparison-based algorithms, that is only to algorithm that can only obtain information on the relative orders of two input elements by pairwise comparisons.
They do not have to be divide and conquer algorithms and they do not have to generate any tree. The lower bound simply follows from the fact that there are $n!$ possible permutations of the input elements and any correct algorithm must be able to output all of them (given the inverse permutation as its input).
This means that the number of branches on the longest computation of the algorithm must be at least:
$$
\log ( n! ) &gt; \log (n/e)^n 
=  n \log n - n \log e
&gt;  n \log n - 1.44 n = \Omega(n \log n).
$$
Also, even in the case of comparison based-algorithms, an absolute lower bound of  $n \log n$ (without the constant hidden in the $\Omega(\cdot)$ notation, as you write in the question) on the number of comparisons cannot possibly exist since, when $n=2^k$, each element in Mergesort is compared at most $k-1$ times, showing that the total number of comparisons is at most $n(k-1) = n \log n - n$.
Your proposed algorithm is not clear to me but, in general,
if you change the model of computation by allowing other operations to be performed in addition to comparisons then the $\Omega(n \log n)$ lower bound does not apply anymore.
For example, given any constant $c$, in the word-RAM model you can sort a collection of $n$ elements between $0$ and $n^c$ in linear time using Radix sort, as long as the chosen word size $w$ allows to write $n$ in a (constant number of) memory word(s), as it is usually the case (it is standard to assume $w=\Theta(\log n)$).