I've had several trailers stolen over the years. One was stolen from our farm buildings - the padlock on the gate being snapped. After that the replacement was kept in the field behind our house, out of sight of the road. It went after the gate chain was bolt cropped. An Ifor Williams flat trailer was taken from our driveway when it was left unlocked for an hour. And why was it left unlocked? Because after the other thefts OH insisted on a fiddly hitch lock, wheel clamp, and that it was chained to a tree. I said that was too much because the trailer was frequently used and no one would be bothered with locking and unlocking everything whenever they wanted to use it. And sure enough that was the case. It was too much trouble. Someone was in a hurry and didn't have time to prat about with all the locks and keys and it was left unlocked for a short time, and stolen. And guess who it was that left it unlocked? Peter (OH).
So for security to be effective it has to be easy to use and for that reason I would NOT recommend removing a wheel because somebody one day will be in a rush and not do it, and the scrotes are always there the one time your security is dropped. I would also not expect your postcode on the roof to be much of a deterrent as you can't see it from the ground. It might help get your trailer back, but better not to get it stolen in the first place. I also doubt if nowadays the police will get a helicopter out just to look for your trailer.
For the last dozen years or so my livestock trailer has been chained to the fence at the top of our drive and the built in hitchlock on the towbar kept locked. In addition my landrover is kept parked in front. This has been most effective and we have had no attempts at stealing. It is easy to lock up as the chain is always attached to the fence, the hitchlock is integral to the towbar, and the keys are always handy on my landrover key ring. I also think it helps that the driveway is very open and visible, whereas the first 2 theft locations were quite secluded so the thieves were not easily seen.
I am now on my 4th livestock trailer, the first 2 being stolen as mentioned. However my third one was never stolen, and that one had my name and phone number on the sides, and a navy blue and a fluorescent stripe all the way round, making it look vaguely police like. I was somewhat paranoic by now and wanted to be able to distinguish it, should I see it driven the other way by (possibly!) a white Transit van. Anyway, that also worked well and after many years I was actually able to keep it long enough to sell it and buy my present one.