Todd - any sub, with careful room integration and REFERERENCE Calibration will work wit your 4 JLB S38's and S-Center setup.
Logic dictates, that the overall 20 Hz to 20 kHz spectrum will be handled with your sub/HT speaker combination.
AV Receiver handles the x-over - you didn't mention the model, so let me use my Yamaha fixed 90 Hz as an example:
VTH-3: from lowest usable Hz - 90 Hz
JBL HT: 90 Hz - 20 kHz.
So from 90 Hz on down, any good / great sub will work. But you have to do the required careful room integration and REF Calibration to blend it seamlessly w/your JBLs.
VTF-3 will work great (provided like Phil said you set it up properly, but that is true of any sub). Another option you can consider is the Adire Dharman for a little less bass at less cost. Or you could try an Adire Allignment Tempest from Acoustic Visions (little more money than Dharman, less than VTF3) with more bass. An Adire allignment Tempest should be on par with an SVS Ultra. I'm currently running something similar to an Adire Alignment Tempest with JBL Studio series.
And as always, unless you don't like the cylinder look plenty of SVS options.