All the parts are almost available... but you might need to sub something like a 2SK170 for the FET used in there as it can be a bit hard to get. But you need to match electronics to capsule - the U67 and U87 mics have some electronic EQ that the KM84 doesn't have.
The TLM103 'sound' isn't terrible - I find it much cleaner than most Chinese mics - but you're right, it's not that nice. Most of the Chinese mics I've heard are tuned with a spitty high-end, and their transformers don't help that much. IMHO, the problem is that the second backplate without a diaphragm is rather strange, and will add phasing artifacts. If you look at the unfiltered frequency response, you'll see a lot of wiggles in the midrange, in terms of off-axis response. The second issue is the TLM103 is a follower design, so the output of the capsule is what you get. It has no place for high-end rolloff, which is there in the U87, and moreso in the U67. To accomodate this, Neumann reduced the number of blind holes in the capsule. This has the effect of lowering the HF response of the capsule - it increases damping on the diaphragm and also the blind holes act as a resonator to give the high-end lift we're used to. The reduced number of them will darken the mic slightly, so it doesn't sound quite like a U87. They probably did this in order to compensate for the lack of HF EQ and transformer in the circuit. At the same time, the 'scoop' at 4kHz isn't as pronounced because part of that is done in the U87 capsule EQ circuit.