Thanks to all who have weighed in on this issue! I found a fix, although I'm still not sure what was wrong before...
To recap, I was using an SMTP server associated with our web host (InMotion) to handle the email functions associated with a Contact Form. Apparently, even though the autoresponder would sucessfully send a response, it would also prevent a redirect from occurring.
This failure appears to be related to a failure during autoresponse, which is shown with this error in the MODX log:
[FormIt] An error occurred while trying to send the auto-responder
email: SMTP Error: data not accepted.SMTP server error: DATA END command failed
I tried switching to a different SMTP server, using the 'smtp-relay.gmail.com' SMTP server associated with a Google account. I am authenticating with a 'Google app password' rather than the two-factor authentication normally required for that account, and everything is working swimmingly!
Apparently, there was some issue with the InMotion SMTP server that is not there with the Google SMTP server. So this is solved. Sorta. ;-) Thanks again!