Spoilers here...

So I've already got Warwick Homestead as a settlement, only to find out Roger is a synth and the Institute is experimenting on the family farm with the intent to wipe them out after.

I don't want to further the Institute's plans, but it seems the only resolution is to not do the quest, or help the synth. Except the logical thing as the farm's benefactor is to expose Roger to the family (traumatizing sure, but at least they know the truth).

Is there any other way to resolve this quest??

Wiping them out comes after the experiment is concluded... not the quest.

You could try not talking the guy down at the end, and see if he kills Roger for you. It is an institute missions so I am going to guess there isn't an easy way to do the mission differently. If the guys isn't essential, killing him will probably fail the mission.

I know you don't want to further their plans, but you do know that particular plan is just to make radiation free food right? It isn't like you would be handing them a massive win or anything if you just finish it.

This is what immediately happens before we get more pod people like in New Vegas.

My problem with this mission is, like everything else Institute related, the complete lack of regard for Commonwealth citizens. When asked about the purpose of the seeds, the scientist even admits the crops will be "probably" harmless (although I get that's the purpose of "experimentation", these are unwilling participants). Also, taking the next step in their experiment puts the remaining Warwicks one step closer to being wiped out. Now that I think about it, it wouldn't be a stretch to believe the Institute would wipe out the Warwicks if Roger was exposed, so maybe the best thing is not to do anything.

I find the whole thing disgusting...

If you hate the Institute that much, why are you agreeing to do these quests for them?

As much as I dislike the Railroad, My Canon Character sides with the Railroad and Minutemen because of Wally. Kill the Morlocks before They develop a taste for Eloi

I mean, yes. The Institute thinks nothing of slaughtering entire towns out of convenience. University Point, for example.