Programs: DL newly minted Platinum, but probably for the last time ever as I'll never make the required spend.
I think the same comment about best site for an ordinary round trip applies to an open-jaw trip - there really isn't any one best site, you have to check a bunch of them. And it is always a good idea to check the actual airline sites as they can have specials not available elsewhere.
While it is a good time for starting to watch, it probably is way too early to actually purchase for next April. Just get a solid idea of going rates. Set some of those "fare watchers" on the sites you use. Keep an eye on things, especially including ITA. Then wait for a sale. For international flights, maybe between 2 and 4 months out, but one never knows.