Transmission

Looking at the symptoms this doesn't match a "NAT table full"-issue.

In a NAT related issue I'd expect connections to either be refused or delayed (until resources are available).
I haven't seen any connection refusal symptoms.. everything is just really slow.
As for the delay mentioned above, it ...

Correct me if I'm wrong, please.
If a NAT table is full, the router responsible for NATing would queue or refuse new connections. Existing connections however wouldn't suffer from the NAT table being full.

What I see on my LAN is the following:
- When I ping my router's LAN IP address, the response ...

See previous post on this subject:
viewtopic.php?f=4&t=9781

Also, what version of Transmission and what OS X version are you running?

What I've noticed in a little experiment:

When I have only one small torrent going (small amount of data in the files that need downloading) time to quit is very small.

When I have large torrents downloading, time to quit is large, but especially the first time I quit, after having added the new ...