[Sprint Samsung Galaxy Note II] tdusen:
I did some comparisons of logcat output from the 1st and 2nd calls. An 8 second lag is coming from trying to set up the video call manager.

Here's the relevant part of the logcat.

08-26 23:48:33.387 I/dalvikvm( 8586): Failed resolving Lcom/android/incallui/vt/CsVTStackStateListener; interface 1418 'Lsiso/vt/VTManager$VTStackStateListener;'
08-26 23:48:33.387 W/dalvikvm( 8586): Link of class 'Lcom/android/incallui/vt/CsVTStackStateListener;' failed
08-26 23:48:33.392 D/dalvikvm( 8586): DexOpt: unable to opt direct call 0x177e at 0x50 in Lcom/android/incallui/vt/VideoCallManager;.mediaInit
08-26 23:48:33.392 D/VideoCallManager( 8586): Instantiating VideoCallManager
08-26 23:48:33.392 D/dalvikvm( 8586): Note: class Lcom/samsung/commonimsinterface/imscommon/internal/IIMSService$Stub; has 165 unimplemented (abstract) methods
08-26 23:48:33.392 D/CommonIMSInterface( 8586): IMSInterfaceForBaseService: startService()
08-26 23:48:33.392 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: startIMSService : [NAME] com.samsung.commonimsinterface.imsstub.common.IMSService, [INTERFACE] com.samsung.commonimsinterface.imscommon.internal.IIMSService, [BIND] true,
[LISTENER] com.samsung.commonimsinterface.imsinterface.IMSInterfaceForBaseService$1@428c38d8
08-26 23:48:33.392 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: bindService to com.samsung.commonimsinterface.imsstub.common.IMSService
08-26 23:48:33.392 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: bindService : com.samsung.commonimsinterface.imscommon.internal.IMSServiceConnectionManager$IMSServiceConnection@42920ba8
08-26 23:48:33.397 W/ContextImpl( 8586): Implicit intents with startService are not safe: Intent { act=com.samsung.commonimsinterface.imsstub.common.IMSService } android.content.ContextWrapper.bindService:529 com.samsung.commonimsinterface.imscommon.internal.IMSServiceConnectionManager.bindService:129 com.samsung.commonimsinterface.imscommon.internal.IMSServiceConnectionManager.startIMSService:63
08-26 23:48:33.397 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: getSystemService : ims
08-26 23:48:33.397 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:33.397 W/ActivityManager( 2590): Unable to start service Intent { act=com.samsung.commonimsinterface.imsstub.common.IMSService } U=0: not found
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08-26 23:48:35.897 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:36.402 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:36.802 D/STATUSBAR-NetworkController( 2965): onSignalStrengthsChanged signalStrength=SignalStrength: 99 99 -87 -45 -120 -1 -1 13 -111 -9 52 -1 2147483647 gsm|lte 0x2040 level=2
08-26 23:48:36.902 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:37.402 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:37.902 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:38.402 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:38.572 D/AudioHardwareTinyALSA( 2008): Entering AudioStreamOutALSA standby mode
08-26 23:48:38.572 I/ServiceKeeper( 2590): In getseinfo pid = 2590 uid = 1000 seinfo= system
08-26 23:48:38.902 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:39.092 D/STATUSBAR-NetworkController( 2965): onSignalStrengthsChanged signalStrength=SignalStrength: 99 99 -87 -45 -120 -1 -1 13 -111 -9 52 -1 2147483647 gsm|lte 0x2040 level=2
08-26 23:48:39.402 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:39.902 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:40.402 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:40.907 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Waiting for IMS Service Connection...
08-26 23:48:41.407 D/CommonIMSInterface( 8586): IMSServiceConnectionManager: Can't connect to IMS Service [ims]
0

Once it finally gives up waiting for the IMS Service connection, the InCallUI renders.