I haven't done much research yet, but the taller stamps with steamship and llama are postage due stamps from the 1870s-90s. There are numerous varieties that include grills and overprints.
These are the only stamps I collect from Peru - specifically because they are related to the US 1869 Pictorials.
Printed by the National Banknote Company shortly after losing the contract to print US stamps, the first Peruvian postage due stamps incorporate the steamship die first used in US #117. Additionally, National used grills similar to those used on the 1869s (I haven't taken the time to measure them, but I believe them to be 'G' grills).
Here's a copy of US 117 for comparison -

-Brian