Puzzle 3235

Could anyone provide insight into the final moves of puzzle 3235? In the following position:

http://en.lichess.org/analysis/r4Nk1/1pp1q1p1/1b2pp1p/1P1pP3/3P4/n1P5/2Q2PPP/R4RK1_w_-_-#0

I played Ng6 (and failed the puzzle), after which the best response for Black is to move the queen. The computer gives +2 after Ng6. The best move is instead Qh7+, which makes sense. However, on Black's next move, the puzzle plays Kxf8, giving up the exchange. This is the top move according to the computer, but it isn't immediately clear why Kf7, avoiding losing the exchange, isn't also playable. The top engine line after this move involves both players retreating pieces in a line that is far from clear or forced. The evaluation difference between Kxf8 and Kf7 is +3 vs. +4.5, respectively. I anticipated Kf7, and it isn't immediately clear to me why this sequence is part of a tactics puzzle. The line after Ng6 Kf7 is very unclear and doesn't produce the sort of forced loss of material or mating threat one usually finds in tactics training.

Thanks in advance for any help!

Can you post your proposed move order?

vs the puzzle solution of:

1. Bxe7 Qxe7 2. Nh4 Na3 3. Ng6+ Kxh7 4. Nxf8 Kg8 5. Qh7+ Kxf8 6. Qh8+ Kf7 7. Qxa8

My order was:

1. Bxe7 Qxe7 2. Nh4 Na3 3. Ng6+ Kxh7 4. Nxf8+ Kg8 5. Ng6

after which White is up the exchange and 5. ...Nxc2 leads to further trades. My issue was that 5. Qh7+ Kf7 is unclear. The engine prefers this move, which leads to the capture of a few pawns after some piece shuffling. I guess a stronger player could calculate the difference between 5. Ng6 and 5. Qh7+, but the line after Ng6 seems very unforced and hard to rule out before playing Qh7+.