As pointed out in the other thread, you do not need a "thick" or heavy flywheel per se. It could be a thin plastic disc with the black/white strips printed on the face of the disc (rather than on the edge). From what I can tell, this is a $1400 MSRP engine so some DIY investment is warranted.
I hijacked what apparently is YOUR photo so as not to violate any rights. So we're on the same page, is this what we're talking about?
And did you manually rotate the motor and count the number of rotations to get 1 revolution of the driver wheel (i.e., the gear-ratio)? Have you found a downloadable MTH soundset for your engine...and do you know ITS gear ratio? Is it important to be able to configure the PS electronics to generate scale-speed and to set the audio to 4-chuffs (or whatever this engine is) per revolution?
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Here's an idea that may apply if for whatever reason you can't pull the gear from the motor shaft to slide on a "flywheel".
Using a motor drawing from a previous post, let's say you want to install a thin disc but can't pull the gear off the shaft. I once had a similar situation wanting to put a tach sensor disc on the wheel axle of an O-gauge truck. I did not have a wheel puller tool so ended up splitting the disc in half and gluing it back on the shaft. In this case the disc had holes around the edge. So this was using so-called "transmissive" IR vs. "reflective" IR as done with MTH striped flywheels. The purpose of the flywheel is simply to provide multiple "pulses" as the motor spins. Whether it's done by bouncing the IR beam off white/black stripes or by shining thru holes is irrelevant. It's the same 3-wires to the PS2/3 tach sensor. Again, you need to do some homework up front if it's important to maintain scale-MPH and/or calibrate to exact number of chuff sounds per driver-wheel rotation. That is you may NOT want 24/24 white/black stripes on your flywheel or disc.