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... because after 2. Kg2...Qd2+ leaves W with 4 options in reply. That often means he's escaping mate. So I spent some time on Qc6+ & R×f5+, without any prospects.

But then I noticed one of W's replies to 1...Qd1+, 2. Ke4, allows 2...Qh1#. That's a clue you're onto something. If 2. Kg2...Qd2+, 3. Kf3...R×f5+. Then if 4. Ke4...Qf4#, or if 4. Kg4...Q×g5#.

Therefore, I returned to looking at the other 3 options following 2. Kg2...Qd2+, to find that two yield instant mates (3. Kf1...Qf2# or 3. Kh1...Qh2#): more good signs! The middle one, (K-g1), can be delayed at best by 3. Re2, then follows 3...Q×e2+, 4. Kg1...Qf2+, 5. Kh1...Qh2#. And there's the #5.

{I had to fix some typos}

27/28 = 96% Very good to see!
But only 28 attempts in 17 years isn't much. 🫤