ginge,
Since you have the 16ga X 7x57R drilling with Einstecklauf, that is the one you should hunt deer with. If you insist on a chamber insert for the Hollenbeck, I recommend .357 mag. and usually use 38 special. You can buy( if you have enough time and money)an insert barrel( Einstecklauf)for full caliber cartridges, such as 308 ( incl. 7x57r). The makers of these, however, won't generally install one over 6.5mm in a drilling (there are exceptions for "strong" drillings-their choice). Plus there would be an extra charge for installing a bushed firing pin. Larger caliber Einstecklaufs are usually reserved for O/U guns, which are considered stronger.
Where were you stationed in Germany? I left there, the last time, in early 82. Did you hunt in Germany? I taught the hunting course at the R&G Club at Kitzingen/am Main, through 1981.
War Eagle.
Mike