I know part of this is the cleaning on a Keith Monks machine they got before applying LAST
Yes, I've found that use of a quality record cleaning machine prior to applying LAST is an absolute necessity. Otherwise, the LAST seems to dramatically increase tics and pops, presumably by "cementing" into place any minute detritus which may be present in the grooves.
I should qualify that by saying that much of my listening is to symphonic music with wide dynamic range, the frequent soft passages making tics and pops more noticeable than on typical pop recordings with narrow dynamic range.
Regards,
-- Al