I think you are right, Sonia, that many Arminians might want to amend proposition (1) in the way you suggest. But I also think these Arminians are confused about the best way to express their own position.
Would not God’s will or desire to save all, as expressed in 1 Timothy 2:4 for example, already include the desire that all sinners willingly (or freely) repent, so that God can prepare them for the bliss of union with him? This is not to say that God would causally override someone’s own reasoning processes or interfere with someone’s freedom in relation to him. For the whole point of the Arminian’s freewill theodicy of hell is to offer an explanation for why God’s own desire in the matter of salvation, although certainly sincere, may never be satisfied in some cases. But even if salvation itself requires a free choice of some kind, or a willingness to be saved, it does not follow that God’s will or desire to save all would itself depend upon anyone’s having the relevant willingness to be saved.
The example of Ted Bundy’s mother, discussed in section 5.1 illustrates the point nicely. Her heartfelt desire for her son’s redemption no doubt included the desire that he willingly repent of his monstrous crimes. But in no way was the existence of this desire itself–the desire that her son willingly repent–conditioned upon her son’s actually being willing to repent. Similarly, even if salvation requires a free choice of some kind, God’s desire to save all already is the desire that all should respond willingly. Whether he will successfully satisfy his own desire in this matter is, of course, a further question, and this further question brings us to proposition (2), which the Arminians reject. It seems to me, therefore, that an Arminian should simply accept proposition (1) as it stands and reject proposition (2).
Put it this way: God certainly desires to save each of us, if we are so willing. But he also desires that we be so willing.
Anyway, those are a few of my own preliminary thoughts. Thanks for a thoughtful response.
-Tom