Interesting observations. Here are some random TH experiences and thoughts, based on a passive bass, that may or may not apply.
1. Aguilar says as AGS gain is increased, bass is "tightened" whatever that means. Overall, I look at the TH/AGS as a simple amp-in-a-box with that characteristic roll off of some highs and deep lows in exchange for drive/cut. I can totally see the appeal in retaining deep lows, however, depending on your songs and how full your band mix gets. The more dense the band mix, the more valuable the AGS for slotting in note intelligibility. In a more sparse band mix, the deep lows are very appealing.
2. One thing to check is dialing back the mids level even more with AGS gain dialed up. It's possible you are hearing that big mid-bump volume and compensating by turning down the output gain, thus less bottom. Cut the mids level more, the pedal volume drops, increase the out put gain to compensate and the perceived low end should increase?
3. I've noticed that the bass control with AGS on works differently than with it off. If you have the mid frequency set low, I think it can overlap with the bass control and the mid level cut negates the effect of the bass control. If you move the mid frequency up at bit (while using mid level cut), the bass control starts to work more normally and you can add in some more deep bass.
4. I totally agree that the TH w/o AGS is a very nice preamp.
I'm just guessing. You are a very experienced worship bassist and TH user so you understand your situation much better, of course.