Honestly, don't buy the packs. They're the most $$$way to do it.
I went from the start of carth/juhani being farmable to 7* off only 3x daily node refreshes and buying from shipments in about a week and a half. Best bet is to be patient and grab every shipment you can until the event, you should still have time
And if you start running close to the clock, refresh your shipments for 50c each day. Worst case is your expenditure for each shard averages to ~100 or so. The 'gambling' packs average to 135 and odds for pulling anyone that will lower it are laughable