I still don't feel I've solved "rampa". I just can't find evidence of "rampa" in Spanish sources as part of a pulpit, nor or "ramp" in English, except in a few modern cases of ramps for disabled preachers, but I presume that can't be the meaning in a Baroque pulpit. I'm suggested "stairs" because I can't see what else it could refer to, but I have no real evidence to support it, except that I have sometimes seen references to the "rampa" of a staircase, meaning the incline. I've added "ascent" as a possibility, because it's used in one of the references cited below, and in a couple of other places:

"In the Cathedral at Trier the ascent to the pulpit is covered by a magnificently ornamented archway with a high decoration at the top."
http://www.newadvent.org/cathen/12563b.htm?fb_comment_id=101...

On "caja" I've had a it more luck. There's no doubt that this means the body of the pulpit at the top of the stairs, in which the preacher stands. Here again are the two examples I posted in the discussion area:

"La caja del púlpito es también octogonal y en los tableros de los lados aparece el escudo del Cardenal."
Just over halfway down the page
http://catedraldesiguenza.es/SIGUINTE.HTM

"Sobre un pedestal finamente labrado, nos encontramos con la caja del púlpito que tiene cinco paños"
With picture
https://www.flickr.com/photos/rabiespierre/2178089737

Well, as I said there, the two words I've found for this in English are "body" and "box", though it's often referred to simply as the "pulpit".

"An artistic conceit largely confined to the 18th century Rococo churches of South Germany was to shape the body of the pulpit as a ship"
https://en.wikipedia.org/wiki/Pulpit

"let the base represent a doorway through which you may see the back of the stair or ascent to the Pulpit, the body of the Pulpit should be hung with crimson and gold lace"
https://books.google.es/books?id=z8wGAAAAQAAJ&pg=PA26&lpg=PA...

"The hexagonal body of the pulpit and spiral stair is original, but the backboard and canopy has been removed."
http://www.scottishchurches.org.uk/sites/site/id/477/name/Dr...

"The pulpit box is constructed of panels of marble slotted into beams and uprights, suggesting origins in wooden furniture."
The Grove Encyclopedia of Medieval Art and Architecture, Volume 1, p. 8
https://books.google.es/books?id=FtlMAgAAQBAJ&pg=PA8&lpg=PA8...

"Inside there were galleries on three sides, the little pulpit box standing on one leg under an immense sounding board."
https://en.wikipedia.org/wiki/Henry_Muhlenberg

There is also at least one example of "case":

"The sunken face of each panel of the pulpit case is trimmed with a carved egg-and-dart molding, and the central panel of the pulpit also exhibits an inlayed IHS"
Louis P. Nelson, The Beauty of Holiness: Anglicanism and Architecture in Colonial South Carolina, p. 190; another examples on p. 135
https://books.google.es/books?id=jpiVsbbFq6oC&pg=PA190&lpg=P...

This last source also uses "pulpit box".