I'd use the same script for the whole process. Just include a flag at each step so you know which part to run:

if (!$part) {
    # Print part 1, which includes:
    <input type="hidden" name="part" value="1">
}
elsif ($part == 1) {
    # Process part 1
    # Print part 2, which includes:
    <input type="hidden" name="part" value="2">
}
elsif ($part == 2) {
    # Rinse and repeat as many times as necessary...
}
[download]

I wouldn't mess with sessions or database storage for something as simple as this.