how do you deal with the difficult Polish consonants?
This is not by any means a professional advice, but a common sense one:The attitude
Firstly, do not resist that Poles and the other half of the world pronunce "j" quite differently than English speakers do. Think about all those Jean-Pauls, Johanns, Jans, Juans. So quit asking "Why don't they do that the English way, the better way?" There is no better way, just different way of expressing sounds in writing, there are different rules for doing that.
Secondly, accept that the basic 24 letters of Latin alphabet are not good enough to represent all complex sounds of European languages, including your native English: both vowels and consonants. And that's why two basic methods were invented: diacritic marks, such as acute, grave, breve, caron, ogonek and digraphs producing new sounds. Some languages consistently stick to one way, others use both methods.
As an English native speaker, you should be familiar with loan words with accents: frappé, naïve, soufflé, soupçon, façade , entrée, exposé, résumé, rosé, piñata, jalapeño.
Stop poking fun of Polish being a language without vowels, as English has also quite a few examples of three or more consonant clusters: split, strudel, angsts, twelfths, sixths, bursts, glimpsed. And it also has plenty of digraphs: <sh>ip, di<ph><th><on>gs, le<ng><th>s, lights (li<silent gh>ts), <ch>eese, <ts>ar.
Accept that the digraphs in Polish are made of pairs other than those in English, but yet they strive to represent similar, although not identical sounds:
<sh>ip ==> <sz>yba
<ch>eese ==> <cz>yta
<ts>ar ==> <c>ar
Don't be discouraged by clusters of Polish digraphs <sz><cz>; these are actually present in English as well, as in "fresh cheese", or "push chair".A transcription method
Do not skip those introductions to Polish pronunciations. Learn at least some basics, like description of palatalization. Yes, some of those seems complex, but what is wrong with this?
a palatalized consonant is one pronounced with a palatal secondary articulation. This means that the consonant is pronounced as if followed very closely by the sound [j] (a palatal approximant, like the sound of "y" in "yellow"). For example, in the Polish word kiedy ("when"), the letters ki represent a palatalized [k], indicated in IPA notation as [kʲ], with a superscript "j". This sound is similar to the combination of "k" and "y" in English "thank you".
You could try using IPA to learn details of Polish pronunciation. The IPA (International Phonetic Alphabet) is a tough beast though, invented by British scientists, originally to represent sounds of English, and later adapted to other languages. "Adapted" is a point in question: Slavic-specific sounds are represented by strange glyphs as if IPA committees did not want anybody to learn Slavic pronunciation.
For if the unprintable IPA phonemic value /t ͡ɕ/ supposes to represent (ć, ci) then thank you very much IPA for not helping at all.
If I were you I would rather concentrate on a special transcriptional system, called Slavistic Alphabet (AS). This is quite nicely described in one of the pages of Grzegorz Jagodziński, A Grammar of the Polish Language, [grzegorj.w.interia.pl/gram/en/gram00.html] and specifically here: Transcription systems used in Polish phonetic and phonology, [grzegorj.w.interia.pl/gram/en/ipa.html].Train your pronunciation
Use one of the several available text to speech tools, which use synthetic voices.
1. translate.google.com lets you listen to single words or short phrases
2. ivona.com has a range of several Polish synthetic voices. But - unless you buy some of their offer - the free version is also limited to short phrases.
3. You can get for free the Polish synthetic voice "Agata", with no such limits, if you happen to own OS X, 10.7 (Lion)