A Bit Up in the Air by Phi

Puzzle explanation

One choice of first and last letters from the clues’ extra words gave “heads or tails”; the other choice gave the apposite anagram “I herald a toss”. In four grid cells the crossing entries could have been either of two words that differed only by an H or T in that cell. The right choices had to be made to complete the same two thematic phrases, each reading diagonally inward from a corner and then turning 90 degrees to the right and reading outward.

Clue explanations

Conventions: * = anagram, < = reversal

No Extra word Answer Explanation
Across
1 Irish ISLAY IS + LAY
5   IMPALAS ALAS after IMP
10   S(H)ARING, S(T)ARING SA + RING
12   PFENNIGS PIGS around FENN(y)
13 hope BIRRS BIS around R(ive)R
14   SEARAT SAT around EAR
15 abuse ANTI AN + IT <
17   EX(H)ORTS, EX(T)ORTS STORE * around X
19   REALM REAL + M
21 road ROUSE GROUSE − G
23   HEALD HEAL + D
25   STENO S + TENO(r)
27   GOSSANS SNAG < around (O + SS)
28   IVOR (l)IVOR
29   LAT(T)ER, LAT(H)ER (RETAIL − I) <
31 accepts ADD-ON ABADDON − AB
33   AROINTED (DERIVATION − (I + V)) *
34 obol CREATES CRETE’S around A
35   SEA GODS S(i)D(e)S around (EA + GO)
36   BLAS(H), BLAS(T) BLAS(é)
Down
1   ISOBARS (SOB + A) in IRS
2   S(T)RINE, S(H)RINE R in SINE
3 relented LAER L + A(n) E(xtra) R(un)
4   ARD-RI ARD + RI(g)
5   INFIELD INFIDEL with D “relocated”
6 affidavit PANE PAN + E
7   ARNAOUT ARNA + OUT
8   ALGATE L in AGATE
9 affidavit SISTS SITS around S
11   GIRRS RS after RIG <
16   AMLA (rur)AL MA(dras) <
18   (H)OSS, (T)OSS (rancher)OS + S
20   LAS(T)ING, LAS(H)ING LAING around S
21 impresario ROSTERS ROOSTERS − O
22   CORNIS(T), CORNIS(H) CORNS around I
23 sandal HOARSE HOSE around AR
24   ESTOP POSE < around T
26   NOOSES NO + POSES − P
27   GLASS LASS after G
28 set-ups IDEAL I + DEAL
30   ENDO END + O(riginated)
32   DATA DAT + A
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