Having done a bit more digging through eastern european sites and updates on BelarusSIG at Jewishgen - looks like family tree has reached an upward endpoint.
Studied the history of Eastern European Jewish surnames and the legal mandates for them from the respective authorities. Prior to 1800 they were not used as most jews lived in shtetls and small communities where Moshe the tailor was all that was necessary for identification. In addition - they resisted taking surnames as they felt that the reason for any mandates would be used for taxation and conscription purposes.
The names were assigned and taken in a multitude of mechanisms - from having them assigned by authorities (sometimes in a rather arbitrary or anti-semitic manner - check history of Weinstein), by profession, by physical attribute or simply by where they came from.
Malashock (Malashok or Малашок) has no meaning with regards to profession or description of either physical attribute or anti-semitic purpose. According to the Eastern European Jewish Surname Dictionary (in Russian) - the genesis of the name Малашок is (according to a Russian researcher) - Малашок (Слуцк). От д.Малашки Вилейск.у which translates to Malashok (Slutsk). From d.Malashki Vileysk.u. From a town named Malashki or Malashko in the district of Vileysk. I believe Malahko is in Belarus.
Anyway - point being - anyone named Malashok in Russia, Ukraine, Belarus, Lithuania or Poland you may find on web searches - may have obtained the surname Malashok, Moloshok, Malashko in the same arbitrary manner as our Movsha (Moshe - to be identified in a minute) and would have no relative ties to us.
Appears the first possible surnamed Malashock that we can track would be found on the revision list documenting 2 Malashoks - apparently brothers Zelik (b. 1779) and Yankel (b. 1776) Malashok who are sons of Movsha (Moshe) - date of birth or any other identifiers unknown. They both had sons also named Movsha - Zelik's born 1803 and Yankel's born 1791.
Currently on Geni we have at the top of the tree - Yakov who died in 1891. According to his death notice in the Slutsk Pinkas (slutsk.org) we have Yaakov Tsvi - son of Mosheh Malashak Kaleinkesh along with son Meir on June 28, 1891.
Also have Sara on 2/15/09 - wife of Tsvi Yakov Malashok.
Our Yakov was married to Sara. His father was named Moshe. Now it gets a little sticky - as we have 2 Moshe Malashok's available - and I'm not sure which one gets the nod. Our relative was married to Rivka who died in an apparent cholera epidemic on 8/9/1855 and death notice reads wife of Moshe Khayat Malashak. Khayat is identifier for tailor.
So - we have a top end of Moshe and Rivka. However, if that Moshe is either Yankel's or Zelik's - we go back another 2 generations - and not sure exactly how to handle that yet - but doesn't look like it will be able to be tracked further.
Also - according to the translator of the Slutsk Pinkas entries - there is a foot note by the name Malashok on Rivka's entry - that Malashok may mean Moshe Khayat was "possibly from Alashak" as there is no meaning to the last name, the letter m (mem) stands for the word "from" so could simply be called "from Alashak." I cannot find any reference to any town Alashak but in Russia there does exist an Alachakh and an Oleshok.
So - we have pretty well documented to Yakov Tsvi's father Moshe. Not sure if his father was Zelik or Yankel - but both point to their father Moshe. Generation prior would not have any surname. To track any further would point to Malashko in Belarus or Alachakh or Oleshok in Russia - and is most likely a dead end. End of story there.
Also - all the Malashoks in Ukraine politics (quite a few) and all other Malashoks or Moloshoks or whatever - are most likely not related. However - no clue if Zelik or Yankel had any uncles and aunts or other siblings. Therefore - are there any relatives still in the old country? No idea.
Also - still wondering about the NY Moloshoks.