That is logically not possible. German sounds foreign to English because it is foreign. How could one achieve that with the same language?
What you can do is exaggerate. Standard German (Hochdeutsch) is a pretty bland dialect. You can use strong local dialects or variants that are still mutual intelligible but have a strong and strange accent. Prime candidates are Bairisch (Bavarian/Austrian), Sächsisch (Saxonian) or any low German variant (Plattdeutsch, or even Dutch which is basically a very early low German dialect). Those variants will not sound "more German" to a speaker of standard German but will have a similar effect.
Another possibility is the exaggeration of properties. In every language there are things that slur over time in colloquial use. You could use old-fashioned out-of-use words (Hagestolz), grammatical constructs (sometimes it is enough to just use the Genitiv instead of Dativ), or nit-picky pronunciation.
Fun fact with the last point: Some people sometimes try to use overly "correct" pronunciation ... and instead use an incorrect one. E.g. the suffixes -ag, -og and similar are all pronounced hard in standard use and hushed in colloquial. Only exception: -ig, this one is hushed in standard use. Pronouncing -ig hard may look correct, but the standard pronunciation is soft (i.e. -ich). (There are dialects in southern Germany where the hard pronunciation is normal, but the standard usage is soft.)
Both variants, using a dialect or exaggeration, are commonly used in dubbed movies. Movies in Germany are dubbed normally. So when an (American) movie deals with interaction with German speaking people and the language barrier can't be neglected you can either use a third language if the story allows it, or you use a dialect or exaggeration. Most of the time a Bavarian dialect is used in serious contexts, a Saxonian for comedic effect.