In this work, we generalize an on-lattice tensor cluster expansion (TCE) framework to an arbitrary correlation order. We show that these generalized tensor cluster expansion features span a subspace of MACE features, suggesting that TCE features can sufficiently pre-screen MACE features for chemical diversity in alloyed transition metal dichalcogenide (TMD) monolayers. We show that, using maximum-entropy subset sampling, we can empirically recover chemical diversity from MACE features using a cheaper TCE representation. We then fine-tune a multi-ACE (MACE) potential with both subsets, and use this potential to predict temperature-dependent vibrational properties in alloyed TMD monolayers with varying chemical ordering. In our approach, TCE features can be used as cheap surrogate features for pre-screening chemically rich configurations using MACE features, allowing for the more efficient finetuning of atomic cluster expansion (ACE) potentials, thus achieving a tractable prediction of finite-temperature alloy thermodynamics on modest hardware.