I have never seen an interpretation of Matthew 7 which depends on understanding κάρφος (kárphos) and δοκός (dokós) specifically as ‘dustmote’ and ‘sunbeam’; in books and websites of biblical exegesis, they are always rendered ‘splinter’ and ‘plank’ or other variations on a joinery theme.
And on the face of it, these books and websites are correct, since the Greek word dokós does not contain the double meaning of English ‘beam’. The core meanings of dokós are: ‘bearing-beam, main-beam, balk or beam, bar (of gate or door), firewood’ [Eulexis: δοκός]; while kárphos is ‘any small dry body, esp. dry stalk, dry sticks of cinnamon, rice-straw, dry twigs, chips, straws, bits of wool, such as birds make their nests of, chip of wood, toothpick’ [Eulexis: κάρφος].
The Greek of the New Testament admits another meaning for dokós, as a kind of meteor, perhaps because of the resemblance between the streak across the heavens and the projection of a joist or rafter. This does indeed mean a beam of light; but the kind of beam needed to carry the metaphor would be αὐγή (augē), sunbeam.
This would seem to close the door on my secondary interpretation—except that the text of Matthew 7 contains clues that the manifest interpretation, of splinters and planks, is intended to mislead. It is suggested in the very first line of the chapter, which reads:
Μὴ κρίνετε, ἵνα μὴ κριθῆτε
[Do not judge, in order that you should not be judged]
This is not consistent with an interpretation of Matthew 7:3 which says we should do a great deal of judging, only provided we start with ourselves. Moreover, the text soon alerts us that in this image something precious has been hidden—‘Give not that which is holy unto the dogs, neither cast ye your pearls before swine [μηδὲ βάλητε τοὺς μαργαρίτας ὑμῶν ἔμπροσθεν τῶν χοίρων], lest they trample them under their feet, and turn again and rend you’ (7:7). This sudden warning does not flow from the verses which precede: it comes out of nowhere. And only a few lines further back the text plainly asserted that we are to envisage the eye as projecting light: ‘The lamp of the body is the eye’ [Ὁ λύχνος τοῦ σώματός ἐστιν ὁ ὀφθαλμός] (6:22).
It may be objected that the text of Matthew does not possess the coherence necessary to read these lines as referring to the mote and the beam. There is indeed a strand of biblical studies which considers the whole of the Sermon on the Mount to be ‘merely a collection of unrelated sayings of divine origin, a patchwork’.[1] But another strand, which given my own line of work I do prefer, insists on the role of the Gospel ‘authors’ as true editors of their material, selecting and arranging the sayings that had come down to them, whether verbally or from another textual source now lost, in order to compose a determinate doctrine. In which case the warning against casting pearls before swine need not, as biblical commentary insists, be considered an arbitrary change of subject.
If the King James translation adds a layer of meaning that was not compassed by the original text, I cannot believe that this was done by accident: one does not by accident produce a metaphor as perfect as the ‘dustmote and the sunbeam’. Nor can I believe that the authors would have consciously added a new layer of meaning that was ruled out by over a thousand years of biblical commentary. Could there be another linguistic device at work in the Greek which would produce the same double meaning as the ‘mote’ and the ‘beam’? This is the theme of the final part.
Notes
[1] W. D. Davies, The Setting of the Sermon on the Mount (Brown Judaic Studies, 1964), p. 1.
Babel editing 
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