I dont see any connection between a /EESC in your recording and the field mapping from LSMW.
The field mapping in LSMW cares about the fields that you recorded, not about the functions.
the processing times and global functions are related to the conversion process of your source data.
if you have 100 records in your source file, then you convert 100 records and get 100 records in the .conv file (if you have not skipped some with logic during the conversion process) .
then you create a batch input session from this .conv file.
so you finally have 100 transactions in the batch input, and each gets cancelled on the last screen, result: noting posted . A lot effort for nothing
You have to record including the SAVE otherwise you will not write anything to the database with such recording