Schedule the scrapes to run in batches (e.g. 20 at a time, once every 6 hours - i.e 80 a day - to minimise the chance of LinkedIn security blocking the IP
I recognise that for someone like me with 1.5k contacts, the process will take ~20 days, but that is ok.
Perhaps email progress report (and a file with a subset of the users) after each run with the updates so far (once we have fully tested this)