The exact wording of the Hebrew is unclear to me.  However what is clear is that this inscription refers to a husband and wife: Gdal son of Micha'el, and Beila daughter of David.
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Steve Goldberg
Jerusalem, Israel
Researching:
Sagan/Shagan family from Veliuona (Velon), Lithuania
Goldberg family from Vidukle, Lithuania
Susselovitch/Zuselovitch family from Raseiniai (Rassein), Lithuania

H(ere) L(ies)
the honorable (abbreviated) Gdil son of Michael
and also her (???) spouse Beyla daughter of David
May their souls be bound in the bonds of (everlasting) life (abbreviated)

the man’s name is likely misspelled and the name should be Gdalya, גדלי׳ rather than גדיל. That carelessness might also explain the error in gender on the third line.  
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David Dubin
Teaneck, NJ

it seems that the second line could read 
and With her husband, Beila daughter of Dovid, however the word used for "With" - אם is mispelled, should have been with an eiyin, ועם

Shimon Sporn of Beit Shemesh, Israel

Researcher # 57380

Perl, Margolies, Itzkowitz, Lehrer families from Kisvarda, Fenyeslitke, Ustilug,

Leher- Rozenberg families of Hrubieszów Galicia Edmondton, London

Sporn families of Marosorozfalu, Rusii Munti, Saszreghin, Kajla, Besztercze-Naszod

Abraham & Stuhlman families from Pecsetszeg & Kozarvar

I agree there are...... <ahem>.... some grammatical/spelling/logical 'inconsistencies'.  That is why I wrote above that it was "unclear to me".
However, the name seems to be Gdal (גדאל). I see an 'aleph' there.  I checked with Hebrew Google and the name does indeed exist, albeit quite rare.  As you said, it could be short for Gedalya - in which case an 'aleph' is more logical than a 'yod'
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Steve Goldberg
Jerusalem, Israel
Researching:
Sagan/Shagan family from Veliuona (Velon), Lithuania
Goldberg family from Vidukle, Lithuania
Susselovitch/Zuselovitch family from Raseiniai (Rassein), Lithuania

Whether it's misspelled or not, it definitely looks like the name on the stone is 'גדיל', which is commonly used as a nick name for 'גד' (Gad). It is often spelled גד'ל, but גדיל could still be a correct way of spelling it - just like the names 'Perl' which is spelled פערל or פעריל, same is 'Shmerel' with שמערל or שמעריל, and many other names..
Also, on the second line it definitely says 'וגם בעלה' which means 'and also her husband', and that must be an error, as it should say 'וגם אשתו' - 'and also his wife'.
All the best 
Yechiel Deutsch 
London 

גדיל גדול can also come from גדליה 
Relly Coleman