Wow!
Many thanks Maskerade, a proper Bank Holiday special, and it's been fun reading through the forum and watching persistence being rewarded. I think this was well worth sticking with, even though I have still for unsolved)
There is very precise and compact clueing, and careful reading of the instructions is needed as well as use of Wikipedia: I recognised the theme and knew some of the themed answers, but most needed research.
( It's not called 'Alphabetical Jigsaw' so the 'every letter' rule does not apply; it doesn't say the parts are in order round the perimeter so; the bottom right-hand square is the right-hand end of the bottom, not the bottom of the right etc).
My way to start filling the grid was to spot that two of the 3-letter answers were hidden in the theme parts, then play with three order to put those parts in the corresponding places.
Like another poster, I cannot parse the second half of 'Grandma...'. I'm also stuck on 'Joined up threateningly...', 'Historian lost deposit...', 'In English wood...' and 'Chap with mum's dog', despite knowing all the initial letters and almost all crossers. Tbh I haven't tried solvers on these so I might get some more, but a couple of hints would be appreciated.