I'd tie it in to the disposal and cut that trap off in the basement (cap it or put a clean-out on the end of that drain line).The dishwasher in the house currently has it's own dedicated P-trap for drainage, it's on the end of a horizontal waste run, and I can see it in from the basement.
The trap itself is tucked in-between the floor joists, so it's clearly lower than the lowest drain on the DW.
Is that a "good" way to drain a DW? I assume there's no high loop, unless it's directly behind the DW. I cannot possibly see any siphon effect happening, due to the fact the drain is lower than the DW, and with the P-trap in place, no sewer gas.....I guess, of course, if I don't run the DW for 6 months the water may evaporate....
I have no problem running the/a high loop to the disposer drain....but if it isn't broke and the drain is there now, I'd be just as happy to keep on using it.
Most new dishwashers come with the "high loop" already installed (clipped to the side of the machine, so that's not really an issue. The problem I have with using the dedicated trap is that velocity can also cause the trap to lose it's seal. The water is pumped out of the dishwasher with some force, so it's conceivable that all the water could shoot right past the trap and down the drain - leaving the trap empty.