>> The flight back to MNL would be at 9:30 ish from Haneda
I think you mean AM, as in the 9:35 AM flight on ANA, HND-MNL Can't connect same-day from Kushiro to that flight. You do need one night in Tokyo to make the connection, as in the thread title, but sounds like you are planning two nights.
This is not my trip, but my plan would be different: one night in an airport hotel (Royal Park for me).
It's February and I would not be inspired to go into Tokyo and 'wander', especially if I tired easily. I would need a must-do (sumo, baseball, sakura, ..., in the spring) but IDK what that would be in February. I definitely would take the limo bus to Shinjuku for two nights if I had a good reason, though I would not be particularly happy about making it back to the airport for a morning international departure.
Spending the last day in Kushiro would give another day for a do-over, relaxing, wandering, finding an onsen. Might be the only good-weather day of the trip. Get to KUH and my winter coat, cap, etc. go into a foldup duffel and I don't open it again until I get home. Two minutes after checkout and I would be at T3. Would be my only trip to Kushiro and would want to take full advantage.
My second choice would be two nights at an airport hotel. Would be free of luggage for the daytrip into Tokyo (or Yokohama. Kamakura, even Hakone for an onsen soak). Wake up at the airport without dealing with any weather getting there.
MNL-TYO in economy is $175 to $250 roundtrip in May, assuming you can fit a seat with 28" to 30" seat pitch. At around 4.5 hours each way that could be a long weekend trip.