FWIW, the issue turned out to be the SIP profile. I think this is what we used, but I'm somewhat unfamiliar with the system still. This is a CSV export of the SIP Device Capabilities for the uWarp.
SIP Device Capabilities,vid1.81,20.0.3.21,
0,1,19,8,24,22,17,13,25,30,35,4,57,36,23,12,5,10,11,56,37,6,26,16,2,55,27,34,18,60,52,53,38,41,29,58,21,54,28,31,32,33,14,9,59,48,49,50,15,39,40,63,64,65,66,67,68,
SIP Device Capabilities Number,Comment,Outbound Proxy Server,Replace System based with Device based In-Call Features,Allow MWI Notifications without Subscription,Enable Digit Collection In Busy Or Alerting State,TLS Only,Allow Device To Use Multiple Active M-Lines,Allow Using UPDATE For Early Media Renegotiation,AVP Only Device,Enable Mitel Proprietary SDP,Force sending SDP in initial Invite message,Ignore SDP Answers in Provisional Responses,IP Media Default,Limit to one Offer/Answer per INVITE,Prevent SDP Renegotiation If Peer Initiated Hold,Prevent the Use of IP Address 0.0.0.0 in SDP Messages,Renegotiate SDP To Enforce Symmetric Codec,Repeat SDP Answer If Duplicate Offer Is Received,Send Answer only after renegotiation is complete,Support CTI Hold/Retrieve,Suppress Use of SDP Inactive Media Streams,Allow Display Update,Allow FQDN for Resiliency,Disable Reliable Provisional Responses,Disable Use of User-Agent and Server Headers,Fail REFER To Keep Call Active On Mid-Call Feature,If TLS use 'sips:' Scheme,Mode for Out-of-Band DTMF,Multilingual Name Display,Override Auto-Answer Headers,Override Auto-Answer Headers With,Q.850 Reason Headers,Remove Anonymous User,Require Reliable Provisional Responses on Outgoing Calls,Suppress Redirection Headers,Use P-Asserted Identity Header,Use user=phone,Enable Distinctive Ringing,Internal Ring,External Ring,Callback Ring,Registration Period Minimum,Session Timer,Session Timer: Local as Refresher,Subscription Period,Subscription Period Minimum,Subscription Period Refresh (%),Invite Ringing Response Timer,Allow Out Subscriptions for Remote Digit Monitoring,Force Out Subscriptions for Remote Digit Monitoring,Creator,Date Created,Created with Version,SIP Device,Vendor Notes,Dial Plan,
1,Uwarp,,No,No,No,No,No,No,Yes,No,No,No,ipv4,No,No,No,No,No,No,No,Yes,No,No,No,No,No,No,RFC 4733 DTMF,No,No,,No,No,No,No,Yes,No,No,<
http://www.notused.com>;info=alert-internal,<
http://www.notused.com>;info=alert-external,<
http://www.notused.com>;info=alert-community1,300,0,No,3600,300,80,0,No,No,,,,,,,