here's what I know about the US '340' model.(1) they were sold in USA for the 1967 model year only (2) they are NOT the same as the home market '340' cars which were not produced until the US model production had ceased..
basically its the same car as a post '66 3.4 Mk2 with a change of badge/model designation.
late in '66, after the BMC merger the cars had cost cutting measures introduced.. leather was dropped in favor of 'Ambla' (ICIs version of vinyl) and the wood veneer was also a less costly version sans the burrs.. no longer 'burr walnut' .leather remained available as an 'option' at extra cost.
every US spec 340 i have seen with auto trans has the old DG trans .
every one i have seen has power steering. Most of the manual versions do not have overdrive fitted. the production number for LHD 340 do NOT include the US models .. over 1,000 of which were sold I believe (they are probably logged as Mk2).
the 'home market ' and LHD export 340 that came out in sept '67 has the following differences to Mk2 :- slim bumpers as per S type design (same item up front) modified rear valance to match the slimmer bumper.. straight port head (as used on XKE etc) ..matching inlet manifold, ribbed valve covers.. 240 also had this set up and the solex carbs were dropped in favour of SUs which gave the cars far nicer driving characteristics..
there is a lot of old guff about 'thinner sheet metal" (untrue) and thinner chrome ..(also untrue) basically the 340 (and 240) was improved mechanically via the straight port head and its inlet manifold.. leather seats, and improved quality veneer could be ordered as an 'option' along with spoke wheels and all the other goodies that were available options for he mk2..including reuter reclining front seats, sliding steel sunroof etc etc .. a few of the last cars produced came fully optioned..even the 240.. none came to USA officially as imports of the mk2 ceased in '67.