A true Arminianism would agree with Limited Atonement, but not in the way defined by TULIP. And Irresistable Grace, as you said, is an imprecise term
We agree regarding the fact that the atonement of Christ's blood Is applied only to believers, in that sense it is Limited. But most Calvinists believe that God will infallibly save all that Jesus died for, which would mean He didn't die for everyone. But in point two of the Remonstrant articles you posted, it says Jesus died for all men. So to say that Arminians believe in Limited atonement is true, but not in the same way that Calvinists hold
People keep saying that Arminius believed in four of the five points of Calvin. This is simply not true. Limited atonement states that Jesus only died for the Elect. The statement below is from Works of Arminius volume two. It is in reference to "did Jesus die for all, or only the Elect". In his answer, he gives two possible ways that statement can be interpreted. Then he rejects one and accepts the other. He rejects the definition of Unlimited atonement which would agree with Universalism, and agrees with the definition of Unlimited Atonement that is held by real Arminians, that Jesus died for all, but that the redemption is only applied to believers.
That Christ has
died for all men and for every individual.
ANSWER
This assertion was never made by me, either in
public or private, except when it was accompanied by such an explanation as the controversies which are excited on this subject have rendered necessary
For the phrase here used possesses much ambiguity: Thus it may mean either that ‘the price of the death of Christ was given for all and for every one,’ or that ‘the redemption, which was obtained by means of that price is applied and communicated to all men and to every one.’
“(1) Of this latter sentiment I entirely disapprove, because God has by a peremptory decree resolved that believers alone should be made partakers of this redemption.
“(2) Let those who reject the former of these opinions consider how they can answer the following Scriptures which declare that Christ died for all men [2 Cor. 5.14]; that He is the propitiation for the sins of the whole world (1 John 2.2); that He took away the sin of the world (John 1.29); that He gave His flesh for the life of the world (John 6.51); that Christ died even for that man who might be destroyed with the meat of another person (Rom. 14.15); and that false teachers make merchandise even of those who deny the Lord that bought them and bring upon themselves swift destruction (2Peter 2.1, 3).
“He therefore who speaks thus speaks with the Scriptures; while he who rejects such phraseology is a daring man, one who sits in judgment on the Scriptures and is not an interpreter of them.
“But he who explains those passages agreeably to the analogy of faith performs the duty of a good interpreter and prophesier (or preacher) in the Church of God.