I'd really recommend joining the yahoo group. I can't speak of the loganlathe group specifically, but I am a member of the south bend lathe group.
The thing is, there are a lot of metal heads out there that might have your part, but if both parties don't know each other, you miss out. Some of these guys tend to hoard parts for themselves, but are also known to sell stuff off and I think some just like to trade up.
For example, I have an 11" south bend. Kinda of a rare animal unlike the 10" and 9" models which are very prevalent. I wanted a chip pan for mine, it was only on the toolroom models. One day, a guy posts a message on the south bend group advertising a chip pan and leg set for an 11" and he was "only" 6 hours away from me (I could have fabricated a chip pan, but a proper one goes "through" the leg at the tailstock end). I jumped on it and drove down to pick it up. I rarely see 11" south bends and parts seem to be even rarer. The guy with the chip pan set said the rest of the lathe got scrapped. He wanted it (the base and chip pan set) for a smaller lathe, but it never worked out right for him.
There is also the home shop machinist board
here
I don't frequent it, but it could also be of some help.
I hear logans are pretty nice machines. How much does Scott @ Logan Actuator want for the replacement parts?