I just did a quick search of the Lithuanian phone directory and found 14 listings for:
Ambotas - 2 males
Ambotiene - 12 married females (IENE ending indicates a married female)
I'd vote for AMBOTAS as the authentic spelling.
The 1920 Census was the first where Lithuania was allowed to be listed as a place of birth. Before that time they'd list Russia since Lithuania did not regain its independence until 1918.
Go to www.maps.lt
to search for the village. Type in only PAS and you get 200+ listing.
The SH sound is represented by S^. The mark over the S makes it sound like SH otherwise is would a regular S sound.
Hope this helps.