Err, Trotsky did negociate Brest-Litovsk because this was the mission the party gave to him, but that doesn't mean he was a proponent of it. He consistently voted against signing a peace, he resigned from People's commissar for foreign affairs as a sign of protest and only in the very last moment when Lenin himself threatened to resign if peace wasn't approved he consented, not even to support it, but only to abstain.
Trotsky's opposition to the treaty was pragmatic, it would be best to see if a revolution in Germany was on the cards first. The Left Communists were the faction that opposed Brest-Litovsk on principle and Trotsky was not with them. Lenin's debate was mostly with them and not Trotsky.
As I said, after Brest Litovsk Trotsky supported continued diplomatic involvement with capitalist powers. He even opposed invading Poland in 1920, partly because it would further antagonise the Entente.
Everybody knows this, but this does not prove how Trotsky would have behaved if he had the power.
Militarisation of labour was put forward when he was in power, the 2nd most powerful individual in the party after Lenin. If anything, his writings in exile are the most opportunist because he was out of office and did not have to face practical issues.
This is just random name-calling of people by Lenin. He liked doing this a lot. I challenge you to find a single person of any significance who wasn't at some point "criticized" by Lenin for some reason or another.
Lenin's testament was hardly random name-calling on the level of his polemics, it was a final attempt to get the party back on track. His criticisms were very well considered because Lenin knew it would be his last political act. And it wasn't just Lenin. I remember reading a contemporary of the two characterise Trotsky as "a man of the state and not of the party". This was why Trotsky came up with the ridiculous "degenerated workers state" theory of a progressive state captured by evil Stalinists at the top, because he could not admit the fact that the house Leon built was rotten to the core.
There is a part of truth in what you say but I don't agree because Trotsky or Stalin means people in power are not the same. Not just one leader at the top, but the whole power structure. Material circumstances were important but I cannot dismiss the influence of the ruling class entirely.
Trotsky and Stalin were both part of the same ruling elite. The power struggle was kept confined to the party leadership, no involvement from the working class as a class.