Yes it did solve the cricket problem. I'm not sure I'd go the grease route unless I couldn't swing the money. The reason is that once the blower starts to go and you're hearing crickets, the blower is placing a substantially higher electrical load on the FSR (Final Stage Resistor). If that part goes, and it doesn't take much, then you're looking at an addition $60.
One of the indications your FSR is going out is that the blower motor can't maintain a constant speed at anything but full speed when it's cold. It kind of pulses.
When you do replace the blower motor for the sake of your own sanity pull the right side (car's right) air-flap assembly out of the car. Pull and replace the blower unit from the right side of the car (passengers side) not the left side like the Bentley manual states.
/// Auto => 6-Spd Manual Conversion | Apex EC-7 | Koni/Ground Control Coilovers | Vorshlag Camber Plates | Meyle HD LCA | PowerFlex bushings | GruppeM CAI | Shark Injector | 6000k HID's and Fogs | BMW European MTechII | BMW Performance Shifter | ACS Mirrors and Rear Spoiler ///