With expert help the riddle what species this grasshopper is has now been resolved:
The grasshopper in your photo is indeed a member of the family Pamphagidae. It is a female of the genus The(unfortunately, it would be impossible to tell which species of Lobosceliana based on a picture alone.)
Species of this genus are highly sexually dimorphic, and while females are completely wingless, the males have long, leathery wings, and produce very loud stridulations.
Phil, and the rest of you interested parties:
I apologise for not thinking to respond to that question simply because it had passed by the time I saw it, but I was just checking my outstanding correspondence and it occurred to me that I never have seen any publication describing an observation I made on a Pamphagid female a few decades ago, Very possibly also in the genus Lobosceliana For all I could tell from memory.
Be that as it may, I found her charming. Having caught her and taken her back to the laboratory for observation, I was nonplussed a day or two later to find one of her droppings (cylindrical, somewhat curved, almost bean-shaped, and in fact the size of a small dried bean) lying in an otherwise empty beaker. Oh well...
Next day I was sitting at my desk, reading, when a small object went whizzing around my office, bumped into something and apparently vanished. Later I found another dropping on the floor! Errr...
I think it was the following day that I happened to be looking at my guest. She began to defecate, which was a rather slow, deliberate process of extruding one dropping. It stopped when perhaps three quarters of the dropping was exposed. Then she calmly lifted one hind leg and with the air of a smoker tapping ash off the end of a cigar, she kicked that hard, little (but in proportion to size, quite large) turd with sufficient force to send it bouncing about my office/laboratory.
On the one hand I found it to be a charming observation of the behaviour pattern, but it also is an instructive example of behaviour adapted to remove faecal material from the whereabouts of the producer. Various insects and some other animals have adaptations, sometimes striking adaptations, for the purpose. Accumulations of faeces often are clues to the presence of prey, and in the wild the droppings of such a grasshopper typically will land several metres away at least, not affording a useful clue to enemies.
In biology I often find it breathtaking to contemplate the sort of thing that can be remarkably interesting (well, certainly interesting to me!)