The text is looking to highlight rare subspecies, and to attract naturalists and birdwatchers to visit. And while "cinciallegra algerina" is fine as a distinguishable type of Blue Tit (looks very different), it perhaps goes rather too far with the concept of a "beccamoschino iberico", which will only be recognisable to the most expert naturalists.
It's the subspecies Cisticola juncidis cisticola (as opposed to the nominate Cisticola juncidis juncidis) and does not appear to have a common or vernacular name (see http://www.biologie.uni-ulm.de/cgi-bin/query_all/details.pl?...

But Umberto has to get across the idea of the biodiversity of this habitat, so he needs to differentiate it from places like the field on the way to my kids' school where there are two Zitting Cisticolas fighting for supremacy at the moment. Just writing Zitting Cisticola will make readers in the know say "So what?" (a bit like the Mediterranean equivalent of saying there are Blackbirds in your garden!)

Fan-tailed Warbler or Zitting Cisticola? If the text is for attracting tourists, then use Fan-tailed, if for scientists use Zitting Cisticola.

So I would suggest a descriptive term such as "Iberian subspecies of Fan-tailed Warbler" or - if space is an issue - "Iberian Zitting Cisticola"

By the way, it's called a Zitting Cisticola because before and during the breeding season the male flies quite high up into the air (so it's often invisible) and makes a huge ZIT ZIT ZIT ZIT ZIT noise throughout the hours of daylight, repelling all other males that dare come into the vicinity.