Derek...
Here is what I know about the various predators and how to eliminate them. I've only dealt personally with nudis and sundails, I have never had spiders.
Nudis..
To completely eliminate them takes time and persistence.
Fresh water method:
If they are removable colonies and you have a QT tank available, the best method is to remove the colonies/frags and dip them for 5 minutes in fresh water, shaking and swishing them liberally to dislodge the full grown. Once that is completed, you look at them VERY carefully and pick off any egg sacs. They are very sticky and are white curly-cue in shape. Once you have the colonies cleaned up put them in the QT tank. Repeat this process every 4 days for 3 or 4 weeks, then once a week or so for another 2 months. The goal here is to get the hatchlings before they mature enough to lay eggs. They hatch out about every 9-15 days and take a week or two to mature enough to lay eggs. Repeated dips and removal will eventually clean the colonies. In the meantime the ones in your main tank will die off going without food for 3 months.
Reef Safe additives: You can couple the above with flatworm worm exit in the dip. This helps shock them and makes them release easier. Tropic Marin Coral Care can also be used, or Lugols solution. These can be used in either fresh or salt water. You can also use Revive in the same manner.
You can also use the above agents in saltwater to help reduce stress, but you will want to extend the treatment period to offset the killing power of the freshwater on these things.
The nuke method:
This method is only to be used with extreme caution and if you have confidence that you can do it correctly.
Obtain Potassium Permanganate crystals. This is a very toxic oxidation agent. You mix 25mg of this per liter of saltwater into a bucket or container and soak the colonies in it for 30-45 minutes occasionally swishing around. Once the period is over, you rinse in more tank water (also in another container) and then either place into QT or back into your tank. The hazard in this is that the agent is poisonous and you should use gloves when handling AND you want to make absolutely sure you get ALL of it off before putting the colonies back into your tank. The stuff is worse than acid in your tank, it will kill everything, corals, fish etc... even a small amount is VERY bad. It is highly effective though and the ONLY currently known treatment that will kill both juvi's/adults and the eggs themselves.
All of these methods would benefit from the addition of a predator in the tank, such as a yellow coris or melanarus wrasse. These are known to eat nudis and are quite effective at picking off any strays. If you use the QT method, I would put one in both the QT and the main tank as you start your war, it will help eliminate them should they pop up.
Using all these methods I have successfully eradicated them from my main tank and 45.
Lets talk losses... while zoanthids and palys are very hardy, the fresh water dips in combination with the other agents are hard on them and you may lose some whole colonies or partials.
I consider the Potassium method less stressful in the long run since it eliminates the need for multiple exposures. If done right, your losses should be minimal. Add to it the fact you do this in tank water and it makes it more effective all around.
Sundial Snails:
The best method for these is fresh water dips AND manual removal. They are much easier to eliminate than anything else. Just go over the colonies carefully once the polyps have closed up in the dip and pick them off. They use a probiscus (snout) to inject into the polyps and suck the juice out, so any polyps they are actively feeding on should be removed or cut away to avoid losing those they are connected to.
Spiders:
Use the same methods for nudis on these, however the wrasses are not known to eat them. There has been some discussion on mandarins or fish that eat snails and stuff eating them, but I have not read of anyone with repeated succsess doing with them. The trick with the spiders is that they will bury themselves into the polyp as it closes. So you will need to watch them carefully for additional signs of being eaten. The good news is that like the nudis and crabs in general, they do not handle fresh water well. So if you are quick and get the colonies into the fresh water before the polyps close and they hide, they will die quickly.
I also suspect that Interceptor will be effective on them as it is kills shrimp and crabs.. or anything with an ectoskeleton that is a crustasean. They are basically crabs, so it should be effective on them too if the dose is big enough. If you have spiders, do this in a QT tank and watch them, the death should come in a few hours and youll be able to see them paralyzed.
Potassium Permanganate will kill them as well....
To answer your question, nudis and sundails will not account for missing polyps overnight, nor spiders from what I have read. You will see half eaten ones, or ones with bites taken out. You'll also see polyps closing up or pinching off etc. That is the sign of these predators.
Whole polyps and sections missing overnight usually indicates either a fish eating them (Hippo Tangs or Fox Faces do this) or one of the predatory worms like the eunice worm will do that kind of damage in short order.
Got photos????