Boletus, that was me a while ago. I had no success running down the leads kindly given to me in that forum.
I knew it, I was a bit sardonic in my last post.
I think it is only fair to disclose all information you have before asking people to get involved in any investigative work on your behalf. You did not do it. You kept it secret - either by design or by ignorance - even though the other forum provided you with quite a lot of useful findings. But not disclosing those facts you demonstrated an attitude that I consider antisocial. People are willing to help, but their time does not come for free, so you should take care of informing them about all alleys already explored - before they start wasting their time on those.
Having said that, I am still willing to give you a little help. The task of reverse engineering of the origin of Morwitch name is quite daunting for several reasons. Others have already given you some examples of possible names of Jews living in Kraków, Krakau - a part of Austro-Hungarian Empire at those times. The original root of Jewish surnames - quite a late invention, forced by administrative authorities - could come from many sources (check it in wikipedia), such as geographical names, professions or standard Jewish first names. I am by no means an expert in these matters but my hunch is that your family name could originate from one of many forms of MAER-, MAIR-, MAJR-, MEIR-, MEIR-, MAR- etc. Spellings are different but they all mean the same. The surname could be formed by adding any form of ending of the type "son of": -ICZ, -ITCH, -ITZ, -ETZ. Hence MAJROWICZ, MAREWICZ, MEIROWICZ, MEIROWITZ for example. But this is just a huge guess here.
I have no time to do other investigative work for you, but you obviously have such time and a motivation. So I suggest the following. Go to the "Consolidate Jewish surname index", avotaynu.com/csi/csi-home.htm type one of possible candidates for the original name, such as MORWITZ and then wait for the response. You will be given pages and pages of candidates, such as those I have shown above, with soundex code and database name. You have to learn what those database names actually mean. I guess "P" could stand for Poland, but I never read any "help" for that search engine, so this is only my guess.
Having collected all that information, you would need to start an elimination process, to narrow down possible candidates, reject names from Italy, etc.
At the bottom of the web page shown above there are dozens of links you may find more useful or specific in your search. For example, there is a link to "Jewish record indexing - Poland".
Good luck.