[Nexus 7 Android Development] AndDiSa:
[MENTION=8559165]OlliWi[/MENTION] the wpa_supplicant.conf located in /system/etc is the default one, the wpa_supplicant.conf located in /data/misc/wifi is the one which is used by your device as long as it exists. If you remove it, the default one will be copied to /data/misc/wifi and later on adjusted with your individual settings.

I've checked your log, too, and I think your issues might be related to the phone app (I don't know from where it comes, probably from the Gapps installation, but it's useless). I suppose something within the initialization process is blocking a thread related to the ui for too much time (probably also because memory is filled up, processor is too slow, ...). The ActivityManager is sending several time SIG 3 to different processes and after some time it's killing itself which then leads to a soft reboot:

05-20 10:20:57.829 479 479 I ActivityManager: Start proc 676:com.android.phone/1001 for added application com.android.phone
...
05-20 10:21:00.132 676 676 E PhoneInterfaceManager: [PhoneIntfMgr] getIccId: No UICC
...
05-20 10:21:35.293 676 676 E CarrierConfigLoader: Failed to get package version for: com.android.carrierconfig
...
05-20 10:22:33.288 479 665 I Process : Sending signal. PID: 676 SIG: 3
05-20 10:22:33.289 676 684 I art : Thread[3,tid=684,WaitingInMainSignalCatcherLoop,Thread*=0x42c84e00,peer=0x12c00af0,"Signal Catcher"]: reacting to signal 3
...
05-20 10:22:33.849 676 684 I art : Wrote stack traces to '/data/anr/traces.txt'
...
05-20 10:22:37.651 479 665 I Watchdog_N: dumpKernelStacks
...
05-20 10:22:39.796 479 665 W Watchdog: *** WATCHDOG KILLING SYSTEM PROCESS: Blocked in handler on ui thread (android.ui)
05-20 10:22:39.796 479 665 W Watchdog: ui thread stack trace:
05-20 10:22:39.796 479 665 W Watchdog: at com.android.server.net.NetworkStatsService.setUidForeground(NetworkStatsService.java:707)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.net.NetworkPolicyManagerService.updateNetworkStats(NetworkPolicyManagerService.java:2578)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.net.NetworkPolicyManagerService.updateUidStateUL(NetworkPolicyManagerService.java:2548)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.net.NetworkPolicyManagerService.-wrap19(NetworkPolicyManagerService.java)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.net.NetworkPolicyManagerService$1.onUidStateChanged(NetworkPolicyManagerService.java:687)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.am.ActivityManagerService.dispatchUidsChanged(ActivityManagerService.java:4315)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.am.ActivityManagerService.-wrap7(ActivityManagerService.java)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.am.ActivityManagerService$UiHandler.handleMessage(ActivityManagerService.java:1770)
05-20 10:22:39.797 479 665 W Watchdog: at android.os.Handler.dispatchMessage(Handler.java:102)
05-20 10:22:39.797 479 665 W Watchdog: at android.os.Looper.loop(Looper.java:154)
05-20 10:22:39.797 479 665 W Watchdog: at android.os.HandlerThread.run(HandlerThread.java:61)
05-20 10:22:39.797 479 665 W Watchdog: at com.android.server.ServiceThread.run(ServiceThread.java:46)
05-20 10:22:39.797 479 665 W Watchdog: *** GOODBYE!
05-20 10:22:39.797 479 665 I Process : Sending signal. PID: 479 SIG: 9
...

I would do the same as [MENTION=2583740]adstraylight[/MENTION] already suggested: wipe everything and start from the begining. There might be also old settings (e.g. /data/misc/wifi/, ...) which might have an influence and the instable behaviour.

[MENTION=8559165]OlliWi[/MENTION]

I had a look also on your second log file: you still started up with WiFi enabled, but I suppose you switched off the router. I noticed, that e.g. Amazon Music and Video were not able to connect and did not start. Blocking such memory and processor consuming applications at startup (as Plex for [MENTION=8074969]Eliastik[/MENTION]) can make a big difference ...