TEMPO Radical Analogue
Aminoxyl (trivial name: a nitroxyl radical or a nitroxide) denotes a radical functional group with general structure $\ce{R2N–O^•}$. It is well known that sterically unhindered aminoxyls baring $\alpha$‐hydrogens are unstable and undergo rapid disproportionation to nitrones and hydroxylamines (Ref.1: A new mechanism for the decomposition of $\alpha$‐hydrogen nitroxides is proposed). For example, decomposition of one of such compound is displayed below (The scheme is from Ref.1):

Sterically hindered aminoxyls without $\alpha$‐hydrogens such as TEMPO are stable radicals. However, it is not clear that steric hindrance at carbon $\alpha$ to nitrogen atom is important in the mechanism. Yet, the lone pair of electrons on nitrogen has played a significant role in the mechanism (Ref.1). Therefore, I speculate that 2,2'-dimethyldiphenylamine, when oxidized to relevant aminoxyl radical, may not be as effective as TEMPO, mainly due to the delocalization of the lone pair of electrons on nitrogen between two 2-methylphenyl groups.
Nonetheless, there are few available aminoxyl radicals, which are more efficient than TEMPO (Both following images are from Ref.2):


The research in Ref.2 has performed catalytic oxidation using few N-oxyl radicals, namely 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO), 2-azaadamantane N-oxyl (AZADO), 1-methyl-AZADO (1-Me-AZADO), 9-azanoradamantane N-oxyl (Nor-AZADO), and 1,5-dimethyl-9-azanoradamantane N-oxyl (DMN-AZADO), in water at $\mathrm{pH} \  10$ on wood cellulose to determine the influence of different N-oxyl radical chemical structures on the reaction kinetics and structures of oxidized celluloses. The reaction time required for complete oxidation of wood cellulose using AZADO, 1-Me-AZADO, or Nor-AZADO was less than $\pu{20 min}$, while DMN-AZADO and TEMPO required $\pu{70 min}$ and $\pu{120 min}$, respectively.
There is also some comparative work has been done in Ref.3, which also showed the superiority of other N-oxyl radicals over TEMPO (Synthetic procedure to prepare Nor-AZADO has been given in the reference; see attached PDF).
References:

Aaron Nilsen,  Rebecca Braslau, &quot;Nitroxide decomposition: Implications toward nitroxide design for applications in living free‐radical polymerization,&quot; J. Polymer Sci., Part A: Polymer Chem. 2006, 44(2), 697-717 (DOI:https://doi.org/10.1002/pola.21207).
Hiromasa Hondo, Tsuguyuki Saito, Akira Isogai, &quot;Preparation of oxidized celluloses in a $\ce{NaBr/NaClO}$ system using 2-azaadamantane N-oxyl (AZADO) derivatives in water at $\mathrm{pH} \  10$,&quot; Cellulose 2019, 26, 1479–1487 (DOI:10.1007/s10570-018-2177-5).
Masaki Hayashi, Yusuke Sasano, Shota Nagasawa, Masatoshi Shibuya, Yoshiharu Iwabuchi, &quot;9-Azanoradamantane N-oxyl (Nor-AZADO): a highly active organocatalyst for alcohol oxidation,&quot; Chem. Pharm. Bull. 2011, 59(12), 1570–1573 (DOI: https://doi.org/10.1248/cpb.59.1570)(PDF).