(Sorry for the late reply; I hope this is still in time to be useful. I've only just seen the question.)

Judging by Google results, "montajista" in this sense is primarily a Latin American term. It refers to the people responsible for the "montaje" of an exhibition, which in English is called "set-up". They are the people who bring the artworks into the exhibition space and set them up in the positions and in the way that the exhibition designer has planned. Set-up comes under the heading of exhibition production.

The curator is responsible for planning the contents of the exhibition. The designer plans how the exhibition is to be arranged, and the "montajistas" set it up according to that plan.

Here's a video in which you can see the "montaje" of a Richard Hamilton show at the Reina Sofía. The people doing it are "montajistas"

"Richard Hamilton – montaje de la exposición / exhibition set-up"
http://www.museoreinasofia.es/multimedia/richard-hamilton-mo...

"El montajista de la muestra es quien instala las obras – se trata de una tarea técnica que puede ser dirigida por un artista o un curador"
http://diariolaventana.com/articulo.php?id=50324

(This very clear explanation is from Latin America, where they call the curator "curador", instead of "comisario" as in Spain.)

I think the best term to use in English for the people who do this job is "installers":

"Exhibitions Installer (Part-time)
The National Gallery of Australia
This position sits within the Gallery’s Exhibitions Section and is part of the team of installers responsible for the preparation and installation of works of art and associated display materials to high exhibition standards. Installers may respond to all areas of the Gallery that require assistance with the installation or handling of works of art and can expect to regularly liaise with Conservation, Curatorial, Registration Travelling Exhibitions and Workshop staff through the Exhibitions Section."

The "montaje" of exhibitions that this refers to is not called "mounting" and the people who do it are not called "mounters". The mounters in Andrew's and Phil's references mount artworks, specially paper works, on supports. The conservation mounters in the British Museum would be called "enmarcadores" in Spanish. Although the word "montaje" can be applied to the highly skilled and specific job of mounting prints and drawings, the person who does it is not called a "montajista":

"La selección de materiales apropiados para el almacenaje y montaje es crucial. El papel puede presentar graves deterioros debido a la proximidad o contacto con materiales ácidos, por tanto, las carpetas, sobres y materiales seleccionados para el almacenaje o montaje deben ser químicamente estables y permanentes. Aunque hoy en día los enmarcadores están más actualizados, existen todavía aquellos que no están conscientes de la importancia de utilizar materiales que garanticen la preservación de las obras sobre papel.
https://elmarquero.wordpress.com/2010/05/17/conservacion-de-...

The fact that the "montajistas" are mentioned in your list just after the "restauradores" doesn't mean that their work has anything to do with conservation. The "restauradores" are mentioned just after the security staff, but have nothing to do with them either,

Finally, "professional" is not redundant and should be included. It doesn't just mean being paid for doing what you do; it means have the skill and experience to do it to a professional standard.