We know love by this, that He laid down His life for us; and we ought to lay down our lives for the brethren. — 1 John 3:16
Greater love has no one than this, that one lay down his life for his friends. — John 15:13
But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us. — Romans 5:8
and from Jesus Christ, the faithful witness, the firstborn of the dead, and the ruler of the kings of the earth. To Him who loves us and released us from our sins by His blood— — Revelation 1:5
WHOEVER = The elect. Only those chosen by God will ever have the desire or ability to believe in Christ.
As for your inserting of the words "whole" and "entire" before WORLD... I don't understand why you did this. The last part of the sentence modifies the first. The only reason to spell out "whole and "entire" would be if your point is that His love for the entire world causes Him to save the entire world. We know that's not true because it's conditional upon belief.
And again... only those who CAN believe, WILL believe. Those are the elect.
I also used to struggle with the idea that God chooses those He saves. I used to think it would be wrong for God to ignore the pleas of salvation for some if they weren't on His list. That's not how it works at all... One cannot believe in Christ unless He/She is enabled to believe in Christ. They will not believe in Him unless they are on that list to begin with. That's the gist of election.