Weighing the Evidence on Grandpa's Birthplace

Six of my Burk (aka Berg/Berk/Birk/Burke) ancestors came to North America from Lithuania. The oldest of the siblings, Abraham, settled in Montreal. All the others lived for decades in New York City.

In birth order, they were:

• Abraham Berk (1877-1962)
• Nellie Block (1878-1950)
• Isaac Burk (1882-1943) - Hi, Grandpa!
• Meyer Berg (1883-1981)
• Jennie Birk (1890-1972)
• Max (Matel) Berk (1892-1953)

Where, exactly, were these Litvak ancestors from? I've been weighing the evidence, following the Evidence Explained principles. Fortunately for me, the evidence is quite compelling in favor of one birthplace for all the siblings.

Of course I'm putting the most weight on primary (original) sources created by "someone with first hand knowledge . . . created at or about the time an event occurred." Primary information (from original sources) tends to be more reliable, even though the person who provided the info may not remember correctly or may answer inaccurately for some other reason.

I've assembled the following evidence about the siblings' birthplace.

1. Abraham Berk's Canadian naturalization petition listed Gordz, Kovno, Russia as his birthplace. When Abraham entered America in 1919 to visit his brother Isaac, he said he was born in Gorst-Kovna-Russia. Abraham provided all this info.
2. Nellie Block never declared any birthplace that I can find, unfortunately. I don't believe she ever married, nor did she apply for Social Security or naturalization. 
3. Isaac Burk told US border officials in 1904 that he was born in Gerst, Russia, when he entered America from Canada. His 1939 naturalization papers and WWII draft registration show Lithuania as his birthplace (Isaac provided the info). Grandpa Isaac was buried in a cemetery plot that's part of the Sons of Telsh society. That adds to the indirect evidence in a small way.
4. Meyer Berg's passenger manifest from 1903 shows Gelsen, Kovno as his most recent residence. His WWI draft record shows Gorsd, Russia as his birthplace; his WWII draft record shows Gorso, Russia as his birthplace. Meyer's naturalization petition from 1920 shows his birthplace as Kovna, Russia. Meyer provided this info.
5. Jennie Birk's 1966 passport lists Lithuania as her birthplace. Her husband Paul Salkowitz listed Gardzai, Lithuania, as his birthplace on naturalization papers, but didn't show anything for her birthplace. Best of all, Jennie's marriage license from 1919 shows Garsden, Russia as her birthplace, info provided by her.
6. Max Berk's 1920 naturalization petition shows Kovno, Russia as his birthplace. His 1906 passenger manifest shows Korst as his last residence. Max provided this info.

According to the Jewish Genealogy Communities Database, nearly all of these places are, essentially, other names for one place: Gargzdai, Lithuania (sometimes not spelled correctly or only spelled phonetically).

This evidence leads me to conclude that Grandpa Isaac and his siblings came from Gargzdai. That's my story, and I'm sticking to it. Plus I'm going to change the family tree so that every one of the siblings shows this as their birthplace.