if you S/S a normal (which you should be able to do) you get 140 points. Since it requires 30 tokens to play you can effectively get 170 points per normal. You need 12k points for the progressive SR, so therefore you'd need to play the normal diff at least 12000/170 = 71 (rounded up) times. This would require 71*30 = 2130 tokens. You should be able to hit every token note on hard dailies (don't worry about not FC'ing, just hitting the notes with books and clearing will be enough) which would net you 16 tokens a song. You'd need to play at least 2130/16 = 134 (rounded up again) normal hards. This would require 134*15 = 2010 LP. Through normal regen you get 10LP/h or 240LP/day.
Since the event lasts another 9 days you'll get around 2100-2200LP through regen during the event. Do note you also gain exp from playing songs, so you'll be able to level a few times which effectively gives you another full LP bar to work with. Combined with the loveca you get through event progression, the 5 from Eli's birthday and the 3 from the extended maintenance you should be able to get the SR rather easily, given you don't waste too much LP.
TL;DR Use provided gems, get 5-7h of sleep every day and you'll get the SR.
EDIT: I derped a bit, updated calculations. It's even easier to get the SR now, since you need to use less LP than you get through natural regen.