For now, it looks like I should cut on the truth ID for the proton only. This will keep all three types of decays, AND it will keep events for which the K+ decays in the detector and is tracked like a mu+. As of right now, there doesn't seem to be a big difference between keeping and cutting these latter events, but will investigate further soon.
Attached is a plot of the MMoffK+ distribution pre- and post the selection of the proton thrown index.

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