"The town appears to be listed as Bapoli.  The father, Leizer, wrote Balta on his declaration of intent ..."

The town may be Bohopil (Bogopol in Russian), which was in the former Podolia gubernia and is now in Mykolaiv oblast in Ukraine. That town was written as "Bapolia" in a family tree in my possession, and it is not far from the Balta region.

You may not find Bohopil on current maps because it no longer exists as a separate town; in 1919, it was incorporated into the town of Pervomaisk (Pervomaysk), along with Holta (Golta) and Olviopil (Olviopol), to make up the present city of Pervomaisk, which is on the Buh river and almost due east of Balta. 
--
Susan Kahan Steeble
Baltimore, MD, USA
Researching: FRIDGANT/FRIEDHAND and variants from Bershad, Ukraine
                      KESSELMAN from Chorna/Okna, Ukraine
                      BUDIANSKY/BUDINOFF and SLUTSKY from Korsun and Zolotonosha, Ukraine
                      KAHANOWITZ/KAGANOVICH from Grodno, Belarus
                      STUCHINSKY from Jurbarkas/Yurburg, Lithuania