Latter-Day Saints (Mormons, or members of the Church of Jesus Christ of Latter-Day Saints), believe that Christ suffered not only on the cross but also in the Garden of Gethsemane.
Consider Luke 22:44:
And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground.
A more detailed description of this suffering is given in the Doctrine and Covenants, in a revelation to Joseph Smith. Christ is speaking here (D&C 19:16-19):
16 For behold, I, God, have suffered these things for all, that they might not suffer if they would repent;
17 But if they would not repent they must suffer even as I;
18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink—
19 Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men.
The prophet Isaiah gave a description of the suffering of Jesus, who was yet to come, in Isaiah 53:
Verse 5 indicates he was wounded, bruised and received stripes, which I believe makes reference to when he was brutally scourged.
5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.
Verse 10: his soul made an "offering for sin":
10 Yet it pleased the Lord to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the Lord shall prosper in his hand.
Verse 12: the phrase "poured out his soul unto death" sounds as terrible a sacrifice as any I can imagine.
12 Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors.
Please also consider the description in "The Purifying Power of Gethsemane". Here's an excerpt:
We do not know, we cannot tell, no mortal mind can conceive the full import of what Christ did in Gethsemane.
We know he sweat great gouts of blood from every pore as he drained the dregs of that bitter cup his Father had given him.
We know he suffered, both body and spirit, more than it is possible for man to suffer, except it be unto death.
We know that in some way, incomprehensible to us, his suffering satisfied the demands of justice, ransomed penitent souls from the pains and penalties of sin, and made mercy available to those who believe in his holy name.
We know that he lay prostrate upon the ground as the pains and agonies of an infinite burden caused him to tremble and would that he might not drink the bitter cup.
As near as we can judge, these infinite agonies—this suffering beyond compare—continued for some three or four hours.
You are right that he did receive the greatest possible reward, but only after the greatest possible suffering.
A final scripture explains that it was an infinite and eternal sacrifice, which we cannot fully comprehend, except by considering the guilt and anguish you and I feel when we sin, and multiplying that by an infinite factor: Alma 34:10,12,14.