There are several things in the original question, so:
If it is saying it's a schema issue, make sure you set the Schema Type option in the Append Tool to "NO TEST", and then you can check the field mapping section to ensure fields actually are mapped correctly. Note: differences in fields are not always easily evident; things like having two text fields with the same field name but different field lengths can even cause issues, so being diligent in checking that 2 fields actually match is important.
Another thing is, when dealing with larger datasets like that, I'd suggest doing it all within a File Geodatabase as far as the appends and any data manipulation and then export to your chosen flat file format. Shapefiles don't always scale that large that well, so any time you're working with really large datasets, it always best to avoid the shapefile if possible.
And no, Object IDs shouldn't be the issue as the append tool should auto re-assign new Object IDs for the newly appended in features. That said, it is important to note that the Object ID will be re-assigned, so if you rely on the existing Object IDs for relationships with other datasets (ex: to use in table joins), you will want to ensure you preserve that Object ID either by copying it to a new field before doing the append or using field mapping options to field map the current Object ID into another field as part of the Append tool.
