Check fan clutch.

You know that the fuel and temperature gauges are related, right?

Both gauges are essentially measuring current from a common, and constant(!) voltage source that is grounded at the sensors, the amperage determined by the resistance at each sensor. If the voltage (let's call it a reference voltage) fed into the sensors' circuits is wrong, so will be the readings of each gauge.

Because the voltage in the car's 12 volt system varies as the battery's charge, load of accessories, alternator's output, and general condition also vary, the reference voltage is the unvarying output of a voltage regulator chip (a solid state, 3-terminal IC mounted on the back of the instrument panel circuit board), arbitrarily selected as 10.0 volts because it has to be below the range of the car's system's voltages in order to perform reliably.

As noted above, if the chip's output is faulty, so will both gauges' readings.

I'm not saying that this chip is your problem, but having noted, "...the fuel gauge was also off: with tank full, needle was at 3/4; when at E dead bottom, there were 5 gallons in the tank...," it is worth considering.

Hello,

Dismantle back the new thermostat and check if its open in boiling water. Should be around 5mm opening. And install it with the jiggle pin upwards (12 o'clock) position.

Hope this helps,
Amarin.

You didn't mention if you pulled the radiator out of the car, and hosed out the cooling fins from both directions.

I had a similar issue with a 1993 240 DL that I bought used in the late 1990's and the radiator fins were clogged with weeds and dirt, that was causing the car to run hot.

In addition to running a radiator flush through the inside of the radiator, you need to make sure that air can flow through the radiator, to cool the coolant flowing through the radiator.

This is also a good time to hose off the a/c condenser, to make sure that system is not blocking air flow to the radiator. You will want to make sure that you have some engine degreaser or Simple Green on hand, in case there is any oily dirt on your cooling system, which I have experienced in the past.

Be sure to take a bottle brush to the overflow tank to get any crud out of that system, and I would also take this opportunity to open the drain cock on the engine block and flush all the coolant and anything else in there, out of the motor.

Finally, I would also disconnect the heater hoses, and run water though the heater core. Make sure that you only have your hose on medium flow, as you don't want to put too much stress on your heater core. After that water runs clear, I'd take an air hose and blow out the remaining water in there so that it does not dilute the new antifreeze.

I refill my cooling system with 1 gallon of 100% antifreeze and 1 gallon of distilled water, adding about 1/2 bottle of each to the overflow tank at a time, so that it mixes well.

Be sure to check back, so that we know what you discover.
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If it needs to be maintained, repaired or replaced on a 1990 240, I've probably done it. '90 240DL, 355,975 miles, will she make it to 400K ?? >>You haven't really worked on a car until you draw blood<< :-}