1. Stay off the NeoBoards. Exposing yourself to other users is in my opinion the biggest risk. And that trickles down to the following (kind of) subpoints:
2. Don't put up any trades/auctions (basically anything where your username is shown to other users lol)
3. Try not to get your username on games hi-score tables
4. Don't own pets with names that are commonly searchable (RWs/RNs)
5. Don't have a big neomall or buy extensively from user shops
Basically, be a hermit on Neopets and play the game as if it's single player. Unless you're xferring literal millions of laundered NPs I think transferring an item in between accounts every so often (definitely spread it out as much as you can control yourself) is fine. It's really when OTHER users start to eye you that you begin to get in trouble. Once people know to keep a look out for you it's so much harder to protect your presence. (Ex. you buy a RW named Puppy. People take note of how your account looks. Some time later you buy an UC that no one has seen before, and it's obvious you haven't been on the PC to trade. That sets off red flags) In my opinion at this point you should continue maintaining regular activity on your account even if it's just logging in to do dailies. Try to get as many site event related trophies as you can as time goes on, to minimize the "gaps" on your userlookup. Those are also annoying things people look out for (even though everyone is guilty of taking several year hiatuses at a time).
Those are just some of my just-woken-up thoughts, would love to hear what other people have to say! Good luck staying under the radar!