Three different ways an English speaker might make the borrowed Polish place name Szczebrzeszynie fit within English phonotactics?
Before you can broach the phonotactics question, you first need to deal with the phonetics. Phonetically, Polish Szczebrzeszynie (which is the locative case of Szczebrzeszyn) is approximately IPA [ʂtʂɛ.bʐɛˈʂɨ̃.ɲɛ]; English doesn't have [ʂ] [tʂ] [ʐ] [ɨ̃] [ɲ]. Best you can do in English is substitute [ʃ] [ʧ] [ʒ] [ɪ~ij] [nj]. The shibilants won't be far off.
Phonotactically, the main problem is the first onset [ʂtʂ]/[ʃʧ] which is forbidden in English. Maybe just substitute [ʃ]? There is also a problem with [bʐ]/[bʒ], but you can get rid of that by moving the syllable boundary from before the [b] to after it.
This results in something like "sheb-zhe-SHIN-yeah" [ʃɛb.ʒɛˈʃɪn.jɛ] which Poles would understand well enough. If you want the nominative case, [ʃɛbˈʒɛ.ʃɪn].
For what it's worth, in Yiddish the city is called Shebreshin (שעברעשין) which fits English phonotactics quite nicely.
NB: In the original tongue-twister:
W Szczebrzeszynie chrząszcz brzmi w trzcinie
The preposition w [f] forms part of the onset of the word Szczebrzeszynie, resulting in [fʂtʂɛ.bʐɛˈʂɨ̃.ɲɛ]. This is one of Polish's famous consonant clusters that will not fit neatly into English phonotactics, I fear.
Before you deal with the phonetic question, you have to deal with the input question: what stimulus would even cause an English speaker to respond with such a word? Is the speaker encountering spoken [ʂtʂɛbʐɛˈʂɨ̃ɲɛ] uttered by a native speaker, or are they seeing "Szczebrzeszynie" written down? English speaker strategies for interpreting foreign spelling are quite variable, but are likely to result in [sɛbrəˈzini].