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All done - helped by having owned a thematic item once, and thus familiar with the full name, and the inventor's (I also still own a more recently invented horizontal item working on the same clever principle, 3 words including one in the thematic item's full name, that most find rather more Marmite in flavour...).
Very clever construction - thank you Hedge Sparrow - with only slightly lumpy graphics (inevitable) and some quite tough as well as easy clueing - but am I alone in finding the clue to 2d very weak? Or am I missing something subtle?

I think 2 down is OK. Unusual use of preposterous but supported by Chambers.

Smithsax -
is 'preposterous' not the anagrind?

I saw 'somewhat' as an instruction to arbitrarily discard 8 letters, leaving 4 as an anagram of the defined entry (admittedly by reverse engineering from the only possible answer).

Am I being very dense? (not unusual...)

quixote - preposterous is a reversal indicator

Ah - I think you have the wrong spelling of the island. Check your unch. Preposterous in this sense means reversed (I think).

Hmmm - I think you may have the wrong one of two candidate islands in the same part of the world.

The correct one is unambiguously a (reversed) inclusion as per wordplay, rather than an anagram.

Preposterous (Chambers, definition 3):

Literally inverted, having or putting the last first (rare)
ORIGIN: L praeposterus reversed, from prae before, and posterus after

2d: OK - I understand that 'preposterous' is here - "rarely" - a reversal indicator, not an anagrind; but no reversal of my entry for 2d - with three confident letters and the fourth unch cycled through the alphabet, reveals to me any word of 4 letters clued by any rational combination of 'Prince', 'Hamlet', and 'somewhat'; and I can only find two real examples of the defined proper-name item that you specify with any different letter in the unch position other than the one I've used - and those work no better - the options give 'clearing the throat', 'Hindu festival' and blank, respectively...

In the first two cases, all the 4 letters are there - 'somewhat'- in one 6-letter word of the clue, so it's ambiguous to say the least.

And where does the Prince come in - is he part of the definition?

As I said, I'm pretty dense.

It doesn't affect the theme, but could get me disqualified for an incorrect entry - so if you can give me just a little more of a nudge it would be much appreciated.

Quixote - you need to look again at possible islands. There is a reversal there which needs Prince as well as Hamlet.
You need the correct island to complete the first instruction.

Oops - my last assertion was an island too far - 'clearing the throat' was a hangover from the anagram period.

Thanks, Smithsax, Candledave and HW7 - I really do get the picture - but the reversal of either island still fails to reveal (to me, any rate) the wordplay in the clue that would resolve the ambiguity in the unch, letter No 3.

Please help me to understand how words 2,3 and 4 work in the clue. I'm incredulous that it's evidently so obvious to everyone else! I need the Doh! -moment.

To be, or not to be...?

Ach!!
The moment I posted I saw it !
Smithsax, Ididn't have the wrong island - it was simply that I was looking for an anagram - and then when you all poited out it was a reversal, only looked at the one word that I'd been concentrating on for the anagrams.
Silly me.
Thank you all for your patient help