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Did they actually hook up a pressure gauge to the fuel line and drive it around? I like your clogged filter theory, and I can think of a couple related causes. A lot of cars have dual or triple-voltage fuel pumps. Battery voltage on start-up and WOT, and lower voltages at othe times. If the pump is going out the fuel line may get full pressure at start-up on high voltage, then slowly bleed off pressure over the next few miles as the pump on a lower voltage cannot keep up with demand.
It could also be the fuel pump controller. As electric pumps age they draw more current. A solder joint in the controller can get hot enough to melt, causing problems. As soon as you stop the car it cools and solidifies. This one can drive you crazy trying to troubleshoot. Look for signs of melting and heat discoloration at the connectors.
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