Thanks for the question: Here’s what you need to know...

By default, MIDI Controllers must default to a specific condition. This condition is agreed upon and is designed so that a recalled program will be initially recalled in a playable state. For example, Sustain cc64 defaults to 0 (Off), PB defaults to +0000, MW defaults to 0, FC to maximum (127) etc., etc.

The Assign Switches default to Off. This is by design.
This being the case, if you want the status to be reversed, you should reverse the direction of the application within the Control Set and set the parameters so they are set as you desire when the AsSw is off (not illuminated). You cannot simply STORE the AsSwitches in the On condition, no more than you could store the MW at 127 or the PB Wheel at maximum... what you can do is reverse the application so that when the AsSw = Off, the Reverb amount you want is recalled and pressing the button does the reverse.

Here’s how to proceed to discover exactly what the Switches are controlling and how to go about reversing them:
On the MODX HOME screen
Press [SHIFT] + [HOME]
This is a shortcut to the “Motion Control” > “Overview” screen, which will point out which of the keyboard mounted controllers are doing what to who...
Press the AsSw1 to highlight to which Part(s) it is assigned. Repeat for AsSw2

Find the “Auto Select” option and activate it (green). This will allow you to move a controller and immediately recall it via it the “Display Filter” —it will show you just what is assigned to the activated controller.

If you press [AsSw1] it will show you all parameters (Destinations) set to change when this button is engaged.
The Destination might say RevSend.

If it is set to a Curve = Standard, and a positive (+) Ratio, reverse the Ratio to an equivalent negative value. This will effective reverse the application of what it is set to do. Or, if it is already a negative Ratio, switch it to a positive value. Now all that remains is to set the Reverb amount you wish to hear when you initially recall the Performance.

Navigate to the REVERB SEND for this Part. You can find it from the Part’s “Control Assign” screen by touching “Effect” > “Routing”
The Reverb Send for the Part is in the upper right corner. Set this to how you like it — with the Assign button not engaged (this is how it will be recalled). And now when press the AsSw1 it will flip to the other condition.

Rinse and repeat for [AsSw2]

Hope that helps... if you get stuck, let us know.

Very Helpful, Thank you.

Speaking about a more general case:

... if using A.SW1/2 for XA Control - there's not necessarily the ability to invert switch meanings like there is in the "mod control" assignments. This is due to XA control's incomplete matrix of relationships to the assignable switch states. So some compromise may be necessary.