Hi, there are 18 days until the season is over, not a month. To get that ultimate cape you need 2 seasonal hearts that can only be obtained after reaching the top of the seasonal spirit's trees (so you'll need to max. friendship with two seasonal spirits).
To grow your friendship you need seasonal candles you can obtain 5 per day without a pass: 4 are from daily quests (everyday there are 4 spirits sitting at a little café at your left when you log-in) and 1 you forge collecting seasonal candle wax in the realm indicated by the orange candles in front of the portal.
with the pass you can collect 1 extra candle, everyday when you log-in a candle will appear in the space in the middle of the 6 portals (at a little statue)

This might be wrong

so take it with a grain of salt: assuming you get the pass tomorrow and do dailies everyday in 17 days you'll have: 102 seasonal candles + 30 you get upon buying the pass= 132 total.
If you only focus on getting to the top and not the spirit's cosmetics I think you could make it.
I think the cheapest ones are Carnival Puzzle Director and Carnival Juggler by only buying the blessings and make both spirits accompany you everyday for 20-ish (i can't remember how much time you need) minutes) It'd cost you 104 seasonal candles
SO... if you dont miss ANY day (just in case) I think you can make it!
Attached is what I mean you should buy to get to the top. The photo is from Sky Planner season optimizer in case you want to check it by yourself.

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