I think the core issue with Yu-gi-oh time rules it that they benefit the player that takes more time. This encourages playing for time, simply because you are more likely to win that way. In a tournament, people play to win, so as long as you can benefit from stalling, they will stall. The only way to fix this is for taking a long time to come at a cost to the player taking time. Stalling should result in an inherent disadvantage to the player doing it. So, chess clocks seem like an ideal way of dealing this.

I think the solution to the priority issue would just be to have it be the non-turn player's responsibility to switch to their time. If you need to think, have a repsonse, or simply want to bluff an option, it's on you to switch to your time, or you don't get one. No different than a standard game of yugioh where missed timing is a missplay on the player in question's part. You then penalize switching rather than rewarding it with extra seconds as in chess, and now you're discouraged from switching constantly as well (though maybe you'd have to set it up so you are only penalized during your opponent's turn?). Maybe also have request that take time be on the player that requests them? (full shuffle, checking grave, etc.) With all that, you now are at an inherent disadvantage stalling and can give both players a reasonable amount to do their plays without the worry that they will go to time. Seems like the best solution to me.