To the many. Not to all.
1 Timothy 4:10 is often used by Universalists.
If God wants to save everyone in what way is He especially saving those who believe?
You just took a verse that Lamb presented saying "all" and argued is doesn't say "all," as in 'every, the whole, every kind of" men. But then, you'd have to in order to make it say "To the many. Not to all."
And 'especially' means, "and most of all" as it does in Galations 6:10, "Therefore, as we have opportunity, let us do good to everyone, and especially to the family of faith."