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Carpet with pad below? That could be a tough go for radiant heat. Here are some examples of R-value for floor coverings

The slab surface temperature is what you want to know and then see what the wood flooring manufacturers allow. If it is glue down flooring, check the adhesive limitations.

Was a heat load calculation and design done for the system? That would show how the carpet dictates the floor btu output.

That 120- 90 is a wide delta, 10- 15 is typical for residential home radiant. It depends on when you measure that ∆. If you could increase the flow rate the floor surface would even out, be more consistent across the surface and may helps.

Increasing temperature or increasing flow will get you more btu/ ft output. This graphic shows the result of the loop temperature from beginning to end as flow is increased, same SWT.

There is a point of diminishing return, from .5- 1 gpm you see a good boost, the red output curve starts to flattens at around 1.5, it is may not be worth the pumping power to get higher flow rates for minimum increase. You have flow meters on the manifold 1/2" loops you could push .75- .80 gpm maybe, through the under-heating loops.

How long are the loops? What tube spacing? Plain water in the system? Your manifold pump will be the limit to what you can actually flow. It's nice to use a multiple speed circulator to get some adjustability.

You want to measure the loop delta after it has been running for a period of time. When the supply and return temperature stabilize, that is thermal equilibrium, measure at that point.

The delta is ever-changing in hydronic systems it is not something that you can "set" the load at any given point in time, how much heat the loops dissipates, that determines the operating delta.

Trust the onsite measurements to determine the output, the universal formulas can deceive as my mentor explains it.