Two years ago on HAL’s “Inca Discovery” cruise, we did the Machu Picchu tour. After getting over the “sticker shock”, we did the “superior” rather than the “standard”. It was worth the extra cost.
The logistics are formidable, and the schedule is tight. I would use a private tour only if it is a pre or post cruise tour. By the way, it looks like you folks on the world cruise get four days and three nights for about what we paid for three days and two nights. (On the Inca Discovery cruise we got off and on at Lima.)
We noticed that HAL charged less for a pre or post cruise tour than the mid-cruise tour that we were on. The only explanation for this inconsistent pricing is competition from private tour companies.
It is an extraordinary, breathtaking experience of a lifetime. Don’t miss it!