Sorry that it took me so long to let everyone know what I did get this issue figured out. I had my SharePoint Submit Data Connection set up to use the default name "form" and I did not check the box for Allow overwrite if file exists. Well of course it would work submitting the first form but it wouldn't overwrite the second form.
In Data Connection I just modified my SharePoint Submit to incude an expression on the file name: concat(projectname, "-", submitter)
Exactly what the above post suggests.
Works perfectly. Thank you to everyone who responded to my question.
Thank you,
Jess