As you say we seem to understand each other a little better, you are right, but I don't think that you understand the argument very well. The reason I say this is that you keep referring to them as always having been there. Now, Koch is not suggesting that a PIE language appeared in isolation on the South-West coast of the Iberian peninsula To quote him "It
should be explained at the outset that an Atlantic hypothesis of Celtic origins does not require a rejection or minimizing of the Indo-European character of Celtic (cf. Meid 2008), nor a relocation of the Indo-European homeland to the west.. "
http://ifc.dpz.es/recursos/publicaciones/29/54/26koch.pdf

The 'corded-ware' culture is not the only Neolithic expansion from the East, there was also a Mediterranean expansion which we can see in the 'impressed ware' culture that is found in modern Croatia/West coastal Greece, Eastern Italian peninsula up to the Po and round to the toe; Eastern Sicily, Corsica, Sardinia, Liguria, South France with further pockets on the Eastern Iberian peninsula and South-West Portugal (beyond the pillars of Heracles).

We also see a cultural/material link between the Western Atlantic peoples during the late bronze age, defining it as a separate cultural zone from both the more general Mediterranean and the Central-European zones.

As for the assuredly Celtic names on Central European coins... The names as they appear on the coins are often shortened, and suffixes etc. are usually deduced. This is important to understand because, obviously, whatever your apriori assumptions about the coin's cultural origins will affect the deductions you make. You also mentioned Ambiorix as a clearly Celtic name, but this is in no way clear. Rix and ambi are PIE roots, riks being a particularly ancient and wide-spread example; rex (Latin), raja (Sanskrit) and in German we see it in OHG as Rih, in Vandalic as Riks, Gothic as Reiks etc.

One other thing to note is that, outside of this alleged Celtic 'home' there are few (if any) terms with bi-lingual roots (the examples you have brought up are Hal-statt and Ba(io)varia. Again, this expectation (that alone among the world's languages) that Celtic was introduced as a partial prefix or suffix into an alien language, ought to be jarring.

Of course if one dismisses Celtic as the language of these areas then what was spoken? A pre-proto-Germanic language (and pre-Balto-Slavic). We may even have the remnants of this extinct language within modern Dutch. Maurits Gysseling proposed, based upon work by himself and Dr. S.J. De Laet a 'Belgian' language (associated with the Belgae); this is based upon endonyms, toponyms and in certain suffixes found in the Dutch language which are not Celtic nor Germanic, but PIE.

The work on this is far from a solid case, however, and I offer it only as a additional question regarding the security of Celtic as originating in the Danube. The endonyms, toponyms and suffixes linked with this are of very questionable heritage in terms of both Germanic and Celtic, but the problem is that any linguistic argument put forth regarding language is, ironically, shouted down by a projected language origin based upon unattested links to a material culture, dreamed up many years ago in the mind of a very earnest but idealistic and romantic academic.