Mission: 8 Tiger, 8 Leopard, 11 Cat

Freebies
Buy Book: +1 Tiger
Ask Dad & Confess: +2 Tiger
Have Tiger and Cat get along: +1 Tiger & Cat
Go out with Cat: +1 Cat
Look for Cat: +1 Cat
Confess to cheating: +1 Leopard
Go on a date & Comfort Cat: +2 Cat

Total:
+4 Tiger, +1 Leopard, +5 Cat

Goal:
4 Tiger, 7 Leopard, 6 Cat
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Observation #1: Asking about Spritual Romance always gives Leopard a point. If we ignore that guaranteed point, then the decision turns into giving a point to one of the spirits.

Modified Goal #1:
4 Tiger, 6 Leopard, 6 Cat
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Observation #2: When seearching for the missing cat, if the spirit you're left with does not share the bed with us, we get a point for inviting them to bed. So it's +2 for the cat searching, and +1 for the cat invited onto bed. This means +1 to Tiger & Leopard, then another +1 to one of them, assuming we restrict ourselves to the first statement.

Note: If we share the bed with Cat, then it doesn't matter who goes searching.

Modified Goal #2 (with restriction):
3 Tiger, 5 Leopard, 6 Cat
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Choices:
Sharing the bed: +3 Someone
Hanging out with Tiger/Leopard: +1 to Tiger/Leopard
Hanging out with Cat (Free hat wash): +1 to Leopard, +3 to Cat
Bento: +1 Someone
Asking about Spiritual Romance: +1 Someone
Search for cat: +1 to Tiger/Leopard
Talk about Cat's suddent departure: +1 to Tiger/Leopard
Accepting the interview: +1 to Tiger & Leopard OR +1 to Cat
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From sheer points alone, hanging out with Cat is a no brainer with the husky hat points:
Remaining with husky hat route:
3 Tiger, 4 Leopard, 3 Cat
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There are two ways to finish up Cat's points:
* Share the bed with Cat
* Share bento, ask Tiger about spiritual romance, and denying the interview

The problem with the second option is that denying the interview gives up a point. Also, sharing the bed with Cat means we can outright ignore the restriction from Observation #2 entirely, so we can settle Cat's points that way without any cost.

Since we accept the interview as well, we end up with the remaining points:
2 Tiger, 3 Leopard, 0 Cat
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We have the following choices left:
Hanging out for a second day: 1 point
Bento: 1 point
Spiritual Romance: 1 point
Search for cat: 1 point
Talk about Cat's suddent departure: 1 point

This results in 5 points left, which is enough to satisify what we need, as long as two are for Tiger, and three are for Leopard.