Put him on a range of hands that he'll raise to 1000 with. Let's say AQ+, TT+.

The possible hand combinations are:
AQ 12 combinations (3 aces left times 4 queens)
AK 9 combinations (3 aces left times 3 kings left)
TT 6 (4 * 3 / 2)
JJ 6
QQ 6
KK 3 (3 * 2 / 2)
AA 3

That's 45 hand combinations of hands he'll raise to 1000 with.

Let's say pushing will get him to fold AQ and TT. Maybe JJ. Let's say he folds JJ half the time. That's 21/45 he folds.

When he calls with JJ-QQ (9/45) you're about 45% to win.
When he calls with AK (9/45) you chop.
When he calls with KK (3/45) you're about 30% to win.
When he calls with AA (3/45) you're about 7% to win.

So it's clearly +EV to push. Almost half the time he'll fold. When he calls you're in a race/chop situation 75% of the time (18/24). It's only in 6 out of 45 hands that you're in trouble. And only when he has aces (3/45) are you almost certain to lose the hand.