Eli Manning was drafted in 2004 Shockey in 2002 and Eli only started 7 games as a rookie in 2004. So the best season you are talking about was Eli's second season in the league.
Eli Manning was not playing very well until his age 28 season in 2009. He was below 60% completion rate until 2008 and didn't throw for more than 4000 yards before 2009. Shockey went to the Saints in 2008. So Shockey never played with Eli passing for 4000 yards.
4,000 yards being just 100 or so passing yards over the average of the last 3 seasons (a new standard).
Eli was throwing closer to 500 times per season than 600 during this time and 600 is the average number for Eli the last 3 seasons.
Manning starts playing 16 games in 2005 and Shockey accounted for 22% of the targets 23.7% of his passing yards that year.
Shockey had some injuries in 2006 and 2007 (missed 3 games played limited in others) if we pro rate for those missed games:
2006 (1 missed game) 123 targets 70 receptions 665 yards 7 TD
2007 (2 missed games) 106 targets 65 receptions 707 yards 3 TD
Shockey's injures follow him with the Saints and he missed more games than that each year for the rest of his career. He does have some improved efficiency stats with Drew Brees because Eli isn't as good as Brees.
Presuming the offense continues to throw the ball around 600 times this season, the pie is bigger than the 557 attempts in 2005 (Shockeys best year with Eli)
Will Tye, Larry Donnell and Jerell Adams had 113 targets between them last season. The Giants added Rhett Ellison in free agency who can be used as a receiver, but he is more of a blocking TE and I expect will be used this way over any of the holdover TE still with the team.
I can see Engram having 100 targets in 2018 in this offense. For 2017 I am not really expecting more than 80 for Engram, Mostly because rookie TE do not usually do much. So that lower expectation applies to all the rookie TE.