My hack found several solutions using just the nine first pins of the DP3T switch, still assuming the switch is break-before-make; a make-before-break switch may short the power supply using these schemes.
It finds 241 solutions (including many variants that differ only by which linked pin something is connected to) in about 0.2 seconds for the nine-pin switch case with a braking resistor, and is about 500 lines of C99. It slows down exponentially as the pin count or labeled pins increase, and is not properly documented or commented at all. At the core, it uses a disjoint set to describe each state, then tries all possible but sane configurations of the pin labels, to find the ones that work, if any. So, a brute force hack.
The hardest thing was to describe all rules to the code; i.e., that the supply should not be shorted in any position, supply should not be shorted via the resistor or via the resistor and motor in the up or down position, and so on. It is intuitively easy for us humans to see a bad situation, but much harder to describe the rules that define whether a situation is good or bad. In total, the hack has 28 cases (a total of 58 equality/inequality tests), for just 9 pins, three links, and 6 labels (P+ P- M+ M- Ra Rb), so it does get complicated rather fast.
First example solution.
Link pins 1 and 4.
Link pins 2 and 9.
Link pins 6 and 7.
Connect motor positive (M+) to pin 5, and motor negative (M-) to pin 8.
Connect power supply positive (P+) to pin 2 or 9, and power supply negative (P-) to pin 6 or 7.
Connect the braking resistor (Ra) to pin 3, and (Rb) to pin 1 or 4.
In the center position, there are three sets of connected pins:
1,4,5: Ra M+
2,3,8,9: Rb M- P+
6,7: P-
Power supply is disconnected from the motor, because negative supply connects to pins 6 and 7, but they are not connected to anything else. Motor negative is connected to positive power supply, but that is okay, because negative supply is not connected to the motor or the resistor. Motor positive and negative are connected via the braking resistor.
In the up position, there are again three sets of connected pins:
1,2,4,5,9: Ra M+ P+
3: Rb
6,7,8: M- P-
Motor is connected to the power supply. One end of the braking resistor is not connected to anything, so it does not affect the supply or powering the motor.
In the down position, there are again three sets of connected pins:
1,4: Ra
2,3,8,9: Rb M- P+
5,6,7: M+ P-
Motor is connected to the power supply with reverse polarity. One end of the braking resistor is not connected to anything, so it does not affect the supply or powering the motor.
Second example solution, not a variant/reordering of the first.
Link pins 1 and 4.
Link pins 3 and 7.
Link pins 6 and 9.
Connect motor positive (M+) to pin 5, and motor negative (M-) to pin 3 or 7.
Connect power supply positive (P+) to pin 2, and negative (P-) to pin 8.
Connect the braking resistor (Ra) to pin 2, and (Rb) to pin 1 or 4.
The three sets of connected pins in each state are:
Center:
1,4,5: Ra M+
2,3,7: Rb M- P+
6,8,9: P-
Supply is disconnected on the negative side. Motor is shorted via the braking resistor.
Up:
1,2,4,5: Ra Rb M+ P+
3,7,8: M- P-
6,9: (none)
Supply is connected to the motor. The braking resistor is connected to motor positive, so it does not affect the motor or the supply.
Down:
1,4: Ra
2,3,7: Rb M- P+
5,6,8,9: M+ P-
Supply is connected to the motor with polarity reversed. The braking resistor is disconnected from one end, so it does not affect the motor or the supply.