I'm not sure whether the topic of "How to Diagnose EFI Problems" has been covered yet... but finding something definitive by using an OBD2 Diagnostic Scanner that can give you some Live, Comparative Data to really confirm that the problem does occur because of poor EFI performance is good beginning. This video will give you a General Idea on how to perform this same test with Common OBD2 Equipment on your SUV, because guessing that to be the case could become OBPITA (One Big Pain In The A**) and STILL not solve the problem:
Your instinct to avoid punishing your New Fuel Pump does you credit. Chemicals created to dissolve thickened, Gasoline Gum and Carbon Deposits that dwell in combustion chambers are meant to be used in as close a concentration as possible. Chemicals like ACDelco TEC (Top Engine Cleaner AKA X66P), Berryman's B12 and the BG-44 type products all work equally well.
However, if dumped directly into the Fuel Tank, they can also soften and dissolve the Rubber Seals inside of the Electric Fuel Pump as well. There are quite a few Threads that cover De-Carboninizing Stuck Compression Rings, Carbon impacted Valve Seats and thickly Carboned Up Piston Heads to restore normal compression and fuel efficiency using the ACDelco TEC via removing the Spark Plugs and injecting the stuff directly into each Cylinder for an extended soak. This must of course be followed by evacuating the Black Carbon Mung that will pool and puddle inside ...before re-installing the Plugs, lest the Goo cause the Rotating Assembly to Hydro-Lock and damage the Engine.
These Harsh Chemical Products should NOT be introduced through the Air Stream as the EFI System is discreetly isolated within its own separate Fuel Line to EFI to Intake Manifold delivery Ports and the stuff will never get to the 'innards' of each Fuel Injector to do its job.
Ordinarily, GM Techs use the GM Tech 2 Hand Held Scanner to perform a "Cylinder Power Balance Test" to determine Cylinder By Cylinder which one is suffering from any performance loss:
The other more laborious method employs the use of an Analog Fuel Pressure Test Gauge and by cycling each EFI... again... Using the Tech 2 to isolate one EFI at a time while the others get disabled... and observing the amount of the Drop in Fuel Pressure individually for each one. In this manner, isolated, misbehaving Fuel Injectors can be identified.
It is too bad that the very involved R&R of the Intake Manifold must be done first before removing the Fuel Rail and Fuel Injectors and either replacing one...or all of them at once if you prefer.... but that is what will be called for if you finally decide to get a Re-manned Set of (6) Injectors and wind up replacing them all as a long term solution. Your profile does not include the Year of Manufacture for your SUV... but armed with that data and search on Amazon will reveal some Vendors who offer these EFIs in Re-Man Sets for around $100 to $150.