If you read the last part of my previous comment, you may already get the answer why your 'dressed up' FED is acting like that. The dressing up/ make-over part or the combining of parts harvested from two or more cameras may account for the less than ideal function.
Why the film tears at the point you described, or at any point for that matter, is often due to over all tightness in the mechanism- from the gears which move the sprocket shaft to the fit of the mechanism in the body which can cause the space where the film travels to go very tight. There are probably dozens of reasons why your film did that.
What appears to have happened in your case is that you continued winding even when the roll reached its end. Easy to do that, especially if you're unfamiliar with these type of cameras. If you feel the tightness at one point, it means that you've reached the end of the roll.
The rewind knob should turn as you wind the film. Sometime you won't see it turning if the roll under isn't tightly coiled. One of the steps involved in loading film (regardless if its from the back or the bottom) is to wind the rewind knob to make the film taut, so it can confirm that the film has been properly loaded when it turns the opposite way.
However, if you've followed all these and still got torn film, then there must be a graver reason elsewhere. When the sprockets are torn, the film won't advance. And when rewound, the torn parts can catch in the cassette and cause the film to tear off.
I can enumerate some which I found to cause such problems:
1. The parts within are dirty or dry. Cosmetic make-overs don't usually pay much attention to how the insides work. I have four such modified cameras. Three had really bad mechanisms which needed to be adjusted and modified. One of the three had to be taken apart to refit the parts.
2. The body and the shutter crate may have come from two different cameras. The space is tight inside Barnack-type cameras. Ill fitting parts will make this tighter and make it hard for the film to traverse within.
One camera I encountered (not a FED but a Shanghai) with this symptom, I had to reshape the body a bit.
3. Another cause for the tightness can be the pressure plate and the springs which hold it up. Is the pressure plate correct? Is it smooth? The pressure plate of the FED easily corrodes, and corrosion, even in the mildest form make the film traverse less smoothly. The springs under the PP may have been installed incorrectly- and this is a common mistake done by repairists. Or the springs may be too bent and push the PP too tightly against the film track.
4. Check the rewind knob too. The shaft goes through a hole on the top plate, and during make overs (stripping, replating, and repainting), the hole can get tighter and cause the rewind shaft to turn with less ease. Or corrosion can also make the knob turn tighter. The rewind knob should turn freely. It should turn with no resistance when there is no film under it.
5. The baseplate may be bearing on the film cassette too. The knob of the cassette (the protruding end of the spool) will rest on the locking latch of the baseplate. If there is something there which restricts the movement of the cassette spool, this will cause film tightening too. Make-overs often involve disassembly of the baseplate too.
6. Is the takeup spool correct for the FED? Though they may all look alike, TU spools do not freely interchange between the FED models, or between Zorki, Leica, or Canon. Some do, some don't.
7. The loading procedure may be at fault. Was the film cut properly? Was the leader length correct? Was it shaped properly?
Most of the possible reasons stated above may require invasive checkup procedures. Unless you do camera repairs, doing them yourself is not recommended. The enclosed shells of the FED cameras do not help much in checking the mechanism's functions.
Another function to check with made-over/dressed up FED is the flange to focal distance. Most made-overs don't have the proper 28.8mm distance anymore. The delicate paper spacers are lost during the process, or not properly measured. Not having this correct distance will mean that the lens or camera won't be able to focus properly.
