What does your flight manual say about operating the oil cooler augmentation systems in LSGI?

My assumption then is that the #1 engine is the only one supplying bleed air for aircraft systems. Assuming everything with the engines check out to be within normal limitations (rigging, air leaks, efficiency, propeller blade angle, etc...), I'd recommend you adjust the Fuel Control LSGI RPM towards the upper limit. Other things you can do if that doesn't work is to re-seal the 5th and 10th bleed air valves and blow out the CIP line from the fuel control fitting into the air inlet housing. Do not adjust the Minimum flow adjustment as a misadjustment there should only cause a flameout when transitioning from HSGI to LSGI. If none of this works, (again assuming all rigging and other checks are correct), the most likely culprit is the fuel control. This is unlikely the cause due to multiple fuel controls involved, but it's not unheard of for multiple components to share the same defect if they were overhauled at the same facility around the same timeframe. Could also just be bad luck. I'm still not sold on taxiing with one single engine in HSGI, especially with a tailwind. I'd recommend only 2 at a time during taxi. If oil temps are difficult to keep under control in LSGI during normal taxi operations and minimal tailwind, you may need to look at that issue separately. If cleaning the coolers with fresh water doesn't fix that issue, either straighten the radiator fins or replace the coolers. Oil cooler augmentation is a great addition if you can afford the modification.

Thanks for your input. No. 1 is on NSGI, the rest at LSGI. Engine efficiency is also quite good. Engines 3 and 4 were running at LSGI for like 5mins before it decayed, probably the only movement they made was moving the throttles slightly forward due to the tailwind factor during taxi that might cause oil temps to rise.

Hydraulic leaks could only affect performance by increasing dirt build-up on the blades. I wouldn't even consider this a possibility unless the compressor efficiency was measured as "low." I would be more concerned about aircrew hydraulic fluid inhalation and A/C system contamination. I would look at your fault isolation manuals for guidance, which has you checking fuel system delivery, fuel control settings, throttle rigging, (and yes compressor condition too). Unfortunately, operational checks don't have the maintenance personnel operate the engine in the way you describe, which makes me think it is "normal" to have unstable RPM at LSGI while manipulating throttles and loading the engines down with multiple bleed air demands while simultaneously dumping air out of the bleed collectors. Just do a full operational checkout of the engines and see if anything is out of adjustment. I would also ask the aircrew to show you where their manuals allows them to taxi with all 4 engines in LSGI. As far as I know, that's not a thing.