By HIIRS I suspect you mean the Hover (Improved) Infrared Suppressers. If so, this is not the reason for the performance difference.
As noted by others on this thread, the Baseline S-70i has the old style metal blade (titanium spar, fibreglass skin with honeycomb core) as fitted on the ‘Lima’ and it does have T700-GE701D engines as installed in the ‘Mike’ - although with 701C ‘Lima’ fuel controls (Not FADEC), so an improvement over the ‘Lima’, but not as good as the ‘Mike’.
In simple terms, think of the S-70i as a UH-60L with a digital cockpit and improved T700-GE-701D engines, but without the ‘Mike’ FADEC control system.
The ‘Mike’ has wide chord composite blades (which provide greater lift) and T700-GE-701D engines with FADEC controls, which provides even more power and therefore more lift, so in essence it is these two upgrades that account for the main difference in performance between the ‘Mike’ and the Baseline S-70i.