Thought: It wasn't the bird-key-capture system in itself that makes JoD's gameplay suffer, it's how the score system is rather ambiguous. In NiD you bust the capture and you receive your time bonus. In JoD you get the key, but when you do it doesn't present you with any immediate bonus, which is off-putting. Then part two of this, as we all know, is how you can't continue around the course afterward. The +time link system JoD has could somehow work with the fact that there is one less mare; +time= longer mares. I guess maybe it would then require tremendous skill to constantly add time, maybe as you make more rounds the time power-up decreases steadily, forcing larger and larger links to obtain any time bonus at all.
My fixed system would be thus- When you get the key you get your time bonus. Then you can keep going around the course as usual until time runs out. Since links now earn you more time, you need a challenge in that the clock will still run down. So in effect it's like a reverse multiplier. As you make more rounds around the mare, each successive run past the Prison will half the amount of time you get back. So by the time you complete half a dozen runs, you'll need to make a 100+ link to even get five seconds back. That kind of thing.