ACROSS
1 Rubenesque in the rear, in turn sharply cut at the middle (6)
ZAFTIG – AFT [the rear], in ZIG{zag} [turn sharply, halved]
4 Recalled a short school vacation, having to sunbathe in Indian house (3,5)
LOK SABHA – reverse all of: A HOL{s} with BASK in
10 Aussie bounder played on maiden’s vacillating (9)
PADYMELON – (PLAYED ON M*)
11 Following one back, His Majesty arrives at Iranian island (5)
QESHM – reverse SEQ., + H.M.
12 Friend to bear down — head to the back (3)
OWL – take LOW [down], and move the first letter to the end. Friend to Winnie the Pooh.
13 Possible source of snag developing from bite, eg in jaw (3-1-7)
WAG-N-BIETJIE – (BITE EG IN JAW*). This is a plant with thorns that “snag” passers by, and not, as I had originally surmised, some kind of wildlife that Australians make sausages out of…
14 Stage door that is closed after game (6)
SCRUTO – SC. [that is] + TO [closed] after R.U.
16 One bent on self-study returning home, crossing Bow Street (7)
NARCIST – reversed IN “crossing” ARC, plus ST
19 Catch Young Conservative, coming from the Right, cheers echoing? (7)
COPYCAT – COP [catch] + Y.C. + reversed [“coming from the right”] TA
20 Revolutionary ideas I’ve partially endorsed (6)
VISAED – hidden reversed in {i}DEAS I’V{e}
22 One promoting growth that’s short blathering about several inches (11)
GIBBERELLIN – GIBBERIN{g} “about” ELL [several inches]
25 Scots brace themselves, winter approaching: the earliest signs (3)
TWA – T{hemselves} W{inter} A{pproaching}
26 Test team moving up the order a US Rastafarian (1-3-1)
I-AND-I – INDIA is the test team; move the final A up in the order to find a Rastafarian word for “us”.
27 An economy, originally in the red maybe finding future (9)
OENOMANCY – (AN ECONOMY*). Oenomancy being divination by wine, one can find the future in either the white OR the red…
28 Perform boring joke, song and dance for food in Asia (4-4)
GADO-GADO – DO [perform] “boring” GAG, + ADO [song and dance]
29 A Finnish company in retreat — no way out of Africa (6)
AIKONA – reversed A NOKIA. This is the Bantu for “no (way)!” Horizons broadened.
DOWN
1 Opening in one way not a thing to start on perhaps (6)
ZIPTOP – ZIP [not a thing] + TO + P{erhaps}
2 Soak once in pool, quietly going about, freezing point outside (6-3)
FUDDLE-CAP – {p}UDDLE [pool – P(iano)] + CA. [about], surrounded by F.P.
3 One waits initially for Frenchwoman to fill kettle, possibly (5)
IMMEW – I + W{aits}, “filled” by MME.
5 Vote in noble men, disposed to be universally kind (14)
OMNIBENEVOLENT – (VOTE IN NOBLE MEN*)
6 Sally’s taking time out, rounding up quiz’s regulars for rising Mexican artist (9)
SIQUEIROS – SOR{t}IE’S, “rounding” U{p} Q{u}I{z}, and reverse the whole of that
7 Brush perhaps with law at first turning to judge’s volunteer enforcers (5)
BASIJ – that’s BASIL Brush; turn the L (for L{aw}) into J(udge)
8 Mark is running in trousers: they won’t support his legs (8)
ARMRESTS – M(ark), “trousered” by ARRESTS [is running in]
9 Drink to pay for: support measuring system (4-4-6)
SLUG-FOOT-SECOND – SLUG FOOT SECOND [drink | to pay for | support]
15 Ruining in the past a branch of the family? (9)
UNCLEWING – or UNCLE WING
17 Yours truly to follow, being old and fully stretched (2,7)
IN EXTENSO – I NEXT ENS O [yours truly | to follow | being | old]
18 Sheltering in Perth in Ashes venue, none leaving, none departing (8)
SCOGGING – in S.C.G. [Sydney Cricket Ground], O [none]; plus G{o}ING [leaving, O (=none) “departing” from that]. Scog means to shelter in Perth, Scotland.
21 Was modelling younger head of ancient goddess in wood? (6)
SATYRA – SAT [was modelling] + YR + A{ncient}
23 Not allowed to have a single name hurt, previously (5)
BANED – BAN{n}ED but with only one N for N(ame).
24 Man regularly taking to north’s provinces (5)
NOMOI – I.O.M. ON [Man | regularly taking], read from south to north
I think it is the first one that I haven’t completed.