You don't need to put everything into a rig. You can simply publish the specific Random Seed generators you need, rename them in the published parameters inspector (if using more than one).
In order to rig an RNG (random number generator) you will need to create a Slider and add at least 20 snapshots. The RNG will not change until a snapshot, so there is no smooth progression from one number to another. You could also create a dropdown menu with a number of different random numbers. It also helps out a great deal to test each random number you add to a rig — sometimes there are variants that are a complete waste of time and you don't want to waste an option on those.
If you stretch out the Inspector column as wide as it will go, it will make adding slider snapshots much easier. To evenly space slider snapshots, set the Range Maximum to the number of values/numbers you will be using. For each slider snapshot, if you double click the blue dot, you can enter the number position it should "pin" to (relative to the Range Minimum and Maximum values you set).
(notice how much room you have when you stretch out the inspector column!)
Once you double click a snapshot dot, you can type in the position then type Return or Enter to accept the value. You must at least type the Return|Enter keys to get out of this — you will not be able to do anything else until you do!
I shouldn't have to say this: make sure you create a new random value for each snapshot! Otherwise Motion will keep applying the same value to each new added snapshot.
I would say at least 20 snapshots is needed for a random number slider. More is better but you will only be able to fit so many snapshots... you might be able to fit up to 50 (you will either not have the room to maneuver, or it will be starting to drive you crazy at that point... 50 is more than enough.) [I'll usually only do 20 and try to pick diverse and interesting random values.]
One last note: you will want to Rig a random number slider (or menu) separately from any other parameter rigging (because of all the individual snapshots needed -- it could really mess things up if you try to add parameters that should "ramp" smoothly between snapshots.)