From the picture in the PDF link the AMP SL jacks look just like the HiDensity ICC jacks, and the BlackBox jack looks like the Leviton jacks.
All I use when I terminate the jacks is my Dracon D714 tool with the 110 blade set to low tension. Never had any problem with terminations... From my experience with 88 and 110 connectors over the years as long as the blade is sharp and proper practices are followed, no problem regardless of manufacturer.
I did not see any picture of the AMP SL tool in the PDF...
....JIM....