- best way to find upgradeable flights so that I can book in Y and use my miles to travel in J, especially for overnight legs

You can do this via the Emirates website. Look for J saver award availability, as this is what is used for Y-J upgrades. Alternatively, get a KVS / ExpertFlyer subscription.

- tips about operational upgrades on this route

Op ups are based on ticket type. So, if you're on a cheap saver ticket, you're unlikely to be upgraded even if you are gold. A flex or flax plus ticket is more likely get an op up.

- any related tips about booking windows and booking directions (e.g., should I start my return trips from Dubai or from London?)

EK are very expensive ex-Dubai according to the Dubai dwellers on here. So, best get tickets from UK.