Transverse-field µSR shifts and relaxation rates have been measured in the non-Fermi liquid (NFL) alloy system UCu5−xPtx, x = 1.0, 1.5, and 2.5. At low temperatures the fractional spread in Knight shifts δK/K ≈ δχ/χ is 2 for x = 1, but is only half this value for x = 1.5 and 2.5. In a disorder-driven scenario where the NFL behavior is due to a broadly distributed (Kondo or Griffiths-phase cluster) characteristic energy E, our results indicate that δE/Eav ≈ (δK/K)T →0 is similar for UCu5−xPdx (x = 1 and 1.5) and UCu4Pt, but is reduced for UCu5−xPtx, x = 1.5 and 2.5. This reduction is due to a marked increase of E with increasing x; the spread δE is found to be roughly independent of x. Our results correlate with the observed suppression of other NFL anomalies for x > 1 in UCu5−xPtx but not in UCu5−xPdx, and are further evidence for the importance of disorder in the NFL behavior of both these alloy systems.