I found out that on the PPSC website you can indeed read documents from the virtual library, I thought you would need a login.
So I read a lot more about this topic and I give some interesting literature links here:
Nicoletti Gonzales: stamps issue of 1874http://www.peru-philatelic-study-ci...874-1879.pdf
Bustamante: catalogue of the issues 1870-90shttp://www.peru-philatelic-study-ci...874-1899.PDF
Dixon: article about the grills (rejillas) of Peru:https://p10.secure.hostingprod.com/...114_1977.pdfhttps://p10.secure.hostingprod.com/...115_1977.pdfhttps://p10.secure.hostingprod.com/..._1977-79.pdf
the article is split into three parts in those links, always quite at the beginning of the journal.
(Don: As this is an important topic also for US classic collectors, I guess this article would be a nice addition to your Stampsmarter library, in a combined way as an own PDF - maybe the PPSC would give permission)
After all the summary could be that there are indeed different grills (as we knew already) and also for different stamp sizes, but many questions remain open.
I try to give my understanding here:
large definitives: 11x15.5mm
small definitives (and small postage due): 10x10mm and 10x11mm
large postage due: 9.5x14mm
No size definition in points is given anywhere, only a correlation of 1cm=12 points, some postage due 13 points.
I also did not find any information in the links above about horizontal vs. vertical ridges.
The grills of Peru are not rare, and are less complicated than the US grills. Even less I understand why no catalogue has ever given the grill types for the issues. It would be easy to add the type to the definitives and postage dues. Also, it should be possible (with a large reference collection) to count the grill points and compare, rather than measuring the mm sizes.
No Peru grill is exactly the same as the US grill types, although National made the grills. So the equipment seems to be made new for the Peru grills.
Another open issue could be paper. National used hard paper, so all Peruvian stamps with grills should be on that paper - again a reference collection could help finding paper differences.
All this topic is interesting and worth being studied more as I am sure that there is much to discover.