I haven't tried it myself, but assuming you have access to PhpMyadmin, a way I would do this is install the new Abantecart version with sample data...export the data...Look at how the columns are setup.
Afterwards, get my old data from the old system, convert all the table data to what the new system wants, re-import.
This doesn't really install anything from the old set and is time consuming, but it's what I'd do since importing and having constant errors is a worst situation IMO than taking the painstaking time to clean up the old data.
Another method of course is to install your previous version of Abantecart. Import all the data in that version, then slowly upgrade every version that was missed to the latest spec. This might be easier and probably worth a look as well since as your system isn't live, if it doesn't work, it may save you a lot of time depending on how much conversion you'd have to do with the 1st method above.