There are 2 on line resources that you should go to. One is the Germans from Russia Heritage Society http://www.grhs.org
which serves Germans from the Black Sea and Bessarabian regions. The other is http://www.odessa3.org/search.html
where you should set the first search box to "St. Petersburg Archives" where you will find numerous Schill in Bessarabia. Lots of other stuff on that site to poke around in as well. It would appear that the Schills were in Bessarabia at least back to the 1830s.
Your biggest challenge in moving backwards will be to bridge the gap between 1896 and the readily available records covering the period roughly 1835 to 1885. The Society may be able to help you with that.
Many ship records show the village of origin. I assume yours does not??? Marriage records of some of the children might indicate a place of birth. Naturalization and military records might also help.