This strikes me as an unusual turn of phrase, perhaps of great antiquity. Does anyone have any information on how old it is, and how such an odd combination of words came about? Are there other similar constructions in English?

OED s.v. be, with relevant citations:

2. To come into existence, come about, happen, occur, take place, be carried out or done; to take its due course, have the appointed period of time.

In earlier use sometimes in present participle with for introducing the period of time; hence for the time being: see Phrases 1b. 

OE (Northumbrian) Lindisf. Gospels: Matt. xxiv. 3 Dic nobis quando haec erunt : cueð us hoenne ðas biðon [OE Rushw. beoþ].
OE Old Eng. Martyrol. (Julius) 24 Sept. 217 Ðu bist dumb oð þone dæg oððæt ðe þis bið [L. usque in diem quo haec fiant].
1423 Guildhall Let.-bk. in R. W. Chambers & M. Daunt Bk. London Eng. (1931) 108 Þe Sheregrinders shull pleyne to þe wardeins of þe Shermen, being for þe tyme.
1429–30 in H. M. Flasdieck Mittelengl. Originalurkunden (1926) 80 Ye sayd xl s..be payd to..ye sayd Elan to ye tym be at scho be a Nun.
a1525 (1520) Coventry Leet Bk. (1909) III. 671 That no persone of the saide Craft Rebuke any of the Maisters for the yer beyng, vpon the payne to pay vj s. viij d.
1773 G. Washington Diary 30 Aug. (1978) III. 202 Calm, Clear, and tolerably warm for the Season being.

And the specific phrase:

b. for the time being (formerly also †for time being): (in office, etc.) for the present time; during the period under consideration; until some other arrangement is made. Cf. sense 2.
1345–6 in J. A. Kingdon Arch. Worshipful Company of Grocers (1886) 124 The Wardenes for the tyme beynge shalle yerly suffre the grapis..to hange Stylle and rype.
1458 in J. Raine Testamenta Eboracensia (1855) II. 225 The covent of the priore..for the tyme beyng, and thair successours.
1464 Rolls of Parl. V. 510 Provided..that neither this Acte nor noon other Acte..be hurtyng or prejudiciall to the Dean for tyme beyng of the Kynges free Chapell.
1523 Ld. Berners tr. J. Froissart Cronycles I. ccxii. 257 The kynges of Englande for the tyme beynge.
[...]
1661 G. Wither Improvem. Imprisonment 51 In Execution to be put, by all Whom, for time being, God shall please to call To be his Prophets.
1713 I. Newton Let. (1976) VI. 51 We are humbly of opinion..that the Master & Worker for the time being, be charged & discharged by his Note.
[...]
1883 ‘M. Twain’ Life on Mississippi xliii. 440 It’s human nature—human nature in grief. It don’t reason, you see. ‘Time being, it don’t care a dam.
1941 A. C. Bouquet Compar. Relig. i. 13 Communist Russia, true to her semi-Oriental ancestry, has for the time being rejected Theism.
1977 J. Crosby Company of Friends xx. 127 The pilot’s one of ours—for the time being.
2007 New Yorker 4 June 80/1 True, for the time being it exists only on paper, as a vague promise.

thanks, lh, all is quite clear now. The expression for the year being was especially helpful in claifying the sense, though I reckon it would raise an eyebrow or two if used today.

Yes, and I’m glad you asked the question because it helped clarify the sense development for me as well.

1883 ‘M. Twain’ Life on Mississippi xliii. 440 It’s human nature—human nature in grief. It don’t reason, you see. ‘Time being, it don’t care a dam. 

Why is there an apostrophe in front of the “T” in ”‘Time being”? Or is that something other than an apostrophe?

Why is there an apostrophe in front of the “T” in ”‘Time being”? Or is that something other than an apostrophe?

It signifies the omitted “for the.”

There’s no apostrophe in any of the editions Google Books shows me.  I have no idea what it’s doing in the OED cite.

It could be a typo from data entry into the OED database, but nineteenth century punctuation is highly variable between printings, with printers making most of the decisions. The OED is citing the first edition, and you really need to get hold of that exact edition to see what it says. The one edition that I can see on the Canadian version of Google Books is from 1901, so that’s no help in telling you what’s in the 1883 first edition.