The Eichhörnchen is the closest we have to a so-called egghorn (read: acorn, compare Eichel; after a languagelog blog posting). Since it does not contrast with any Horn on pragmatic grounds, it is strictly speaking not a diminutive. Animals with hand-like paws tend to be antropomorphized more easily, eg. Wasch-Bär(chen?), and the miniature size of it is readly contrasted with more intimidating animals, eg. Bär / Wunderbärchies. So, the diminutive is fully warranted on underlying lexical grounds, but the stem is a cranberry morpheme (like crane-) and *hörn actually is not a morpheme at all, so eichhörn- is monomorphemic mutatis mutandis. That might make it a pseudo-diminutive in an etymological sense.
The quest as per OP is to show that this extensive definition generalizes over a compact set in the lexicon. This can be made stratified in the ideal case that evidence has been dated, eg. from loan words. The Küch'lein might belong here if you accept -ch- as a contracted affix, cp. En. cooky (from Dutch). Albeit, the etymology of Kuchen is remarkably uncertain. This is incident to Plätzchen, which is a loan into high High German, but you can also find Printen. A wide range of pane words remains ultimately unsolved, e.g. pizza. Cp. Flammkuchen. Bread backing is old, but not stone old in the former pastoral communities. So, this is an unriable data-point.
*k develops to German h, French ch (Hund, chien, Latin canis /k/) if from Germanic, but c /ts/ from some layer of Latin, Dezember, Decembre, as well as from *t (sweetheart, Süße, Herzilein). So it could be either from *plat- (as is prefered) or from *plak- (cp. Flammkuchen, Flach, Fläche(n)) with a more or less phonetically conditioned Reibelaut. It bears mention that Platt schnacken corresponds to Snack naschen (not to toot my own horn), cp. En. fnaese "sneeze" for the sound change.
The Knöllchen "citation" is notable as well. Although it could to mean knüllen, and Knolle may be the etymological root (eg. root bunch, bunch up), it works on a rather sound-symbolic level. It is remarkable that kn- covers a wide range of Lautmalerei, some of which connecers to terms like Knecht, Knabe, etc. that may be frequent in appellative.
After all, cp. En. -kin, which is the most likely exponent of the same root in the geneological tree. The tree is broad enough to allow some overloaded morphemes. Eg., a prosodic stop would be allowable before ch because underlying vowels condition its contrastive distribution /x ç/, and a (glottal) stop is allowable before vowel initial syllables. If this stop may appear between the preceeding stops onset and release because the apex is tenuis, then 'tchen is allomorph to -chen and the n-stem may be explained via Kroonen on Kluge's law as indicated by the geminate. See also Dutch plantjes, cp. Irish clan.