Hello Gene! You're definitely not bugging me. I'm very happy to do all that I can to help contribute to your noble cause. Unfortunately, I have very little else to offer though. My records just aren't as recent as you need.
I did find the obituary of Jeremiah's father, which lists that he had four sons. I am unable to find anything on the unknown son. The other two sons, Russell Day Van Sickle (1890-1967) and George Stanley Van Sickle (c.1902-after 1929) appear not have had any descendants.
Although I am uncertain where the younger generation of this family is buried, the older Van Sickles are buried in Elmwood Cemetery in the town of New Brunswick. Sometimes cemeteries have obituaries on file. I think it's worth a shot. Their phone number is (732) 545-1445.
There is also a volunteer at Random Acts of Genealogical Kindness for Middlesex county. You can find her email through the link below:http://www.raogk.org/newjersey2.htm
I'll be sure to keep my eyes open for anything that will help. Keep in touch, Gene.