Low gain avalanche detectors (LGADs) deliver excellent timing resolution, which can mitigate mis-assignment of vertices associated with pileup at the High Luminosity LHC and other future hadron colliders. The most highly irradiated LGADs will be subject to 2.5 × 1015neq/cm^2 of hadronic fluence during HL-LHC operation; their performance must tolerate this. Hamamatsu Photonics K.K. and Fondazione Bruno Kessler LGADs have been irradiated with 400 and 500 MeV protons respectively in several steps up to 1.5 × 1015neq/cm^2. Measurements of the acceptor removal constants of the gain layers, evolution of the timing resolution and charge collection with damage, and inter-channel isolation characteristics, for a variety of design options, are presented here.