You made a good find that "tost" is the past participle of "toss", but I don't think "contention-tost" means that contentions are tossed away. More the opposite, in fact: the men are tossed by contention.
Firstly, consider the context. The flute learns "a stormy note / Of men contention-tost, of men who groan": in conjunction with storminess and groaning, it doesn't sound like "contention-tost" is something peaceful and conciliatory.
Think of it by analogy with the word "storm-tossed". A storm-tossed sea is one tossed by the storm - wild and dangerous. Similarly, a contention-tossed man would be one tossed by contention - argumentative or bellicose, perhaps.
Finally, this isn't the only appearance of the word "contention-tost" in English literature. Let's check a few more examples of the word being used in context:
Thus Corinth had its partisans of old,
With zeal as flaming as their love was cold:
Some cry'd up Paul, and some Apollos prais'd,
And some for Cephas clam'rous voices rais'd;
Till on the waves of fierce contention tost,
Their ark was founder'd, Christ and Truth were lost!
-- Timothy Touch'em, "The Age of Frivolity" (emphasis mine)
When waters cover'd all the Earth,
When Ocean's deepest Bed was driven
With all his tow'ring waves to Heaven,
And in the fierce Contention tost,
The bounds of Sea and Land were lost
-- William Morgan, "Long Ashton" (emphasis mine)
So there we are. After all this evidence, it seems quite clear now that "men contention-tost" means men made unruly by contention.