You can accomplish this by using ModelAddition actors. A good one to duplicate is the Fungal Growth model, so I'll assume you do this.
First, set the model to whatever it is that you want (I did an archon in the example). Then go into Events +. Here you can delete the events corresponding to the Fungal Growth behavior and add your own 'Create' event. So make a new event for 'Unit Birth', set the source to Zergling (or PsionicZergling or whatever). Then for the term make it 'Create'. Now the actor will spawn on the Zergling.
You will notice there is also an ActorCreation event that sets the scale. You can use this if you want. It seems as if you should be able to use a similar method to set the height, but I can't get it to work.
For now, look at Host Site Operations +. It should say SOpAttachCenter. This is telling the model to attach itself to the center attachment point on the Zergling model. If you want to see all the attachments, you can go to the previewer. You can attach models to other models to see where the points are. If you want to change the location, you have to put the name of the appropriate site operator, which is a type of actor. You can look through them in the editor.
Finally, this is can be used to set the height offset. If you look, you will notice an operator called SOpHigherBy5. You can duplicate this to apply any offset to the actor. Use it by adding it to the host site operations: "SOpAttachCenter SOpHigherBy5" with the appropriate substitutions. There are other site operations that can do a lot.
Also, the editor will show these changes when you place a new model, which is useful. I made an example with site overhead and a slight decrease in height. It makes an archon ride a zergling.
Edit: I forgot to mention you should add an event 'UnitDeath.Zergling : Destroy' to get rid of the actor.
I'm not sure what is wrong without more info. If it didn't show on the unit, it is probably because you didn't update the Events + to point to your unit. My demo was for the base Zergling unit. I attached a picture with the fields for Events and Host Site Operations.
Note that the actor SOpLowerBy1 is an actor I created by duplicating the standard actor SOpHigherBy5. There is a field in that actor called local offset you can modify.