You're right - Scroll Text does override Sequence Text. So... build your own Scroll Text!
IF you are building this project as a "Motion Project" or Generator, then you need to create a Rectangle with the same height as your project. If you are building this as a Title or Effect, then you have an object with Size attributes to use. (Center it — at least in the Y direction.)
To your Text Object, add 2 Behaviors — Basic Motion — Align To behaviors.
To the bottom one in your list:
Add the Shape or background object to the drop well.
Set Align "Text Object" to Top
Set To [shape object] to Bottom
To the top Align To in your list, add the background object to the drop well and do the opposite
Align "Text object" Bottom
To [shape object] Top.
Set the Transition parameter to Custom
Set the Custom Amount to 0%
Right click on this Custom Amount parameter and Add Parameter Behavior — Ramp.
Set the Ramp End Value to 100 (%).
You can adjust the animation start and end with Start Offset and End Offset Parameters.
You can apply your Sequence Text Behavior and Wriggle behaviors as you like.
For horizontal placement of your text, use a Rectangle to Align To, set its opacity to 0 and use the Position X parameter for placement. You could also Rig the Align To Offset X parameters if you prefer.
You may notice Y position speed-ups/slow-downs in the animation because the Text Object bounding box will change with the Sequence Text parameters you applied Wriggle behaviors to. I'm not sure it will make any difference to the viewer since everything will be jittering around anyway :D
Let me know if you run into trouble.