Default Flashable (via recovery) VNC server? Or similar software?

Hey guys,

My Nexus 4 screen+digitiser are dead (I replaced the whole phone with a Moto G because it was nearly the same price as repair). I changed recovery from TWRP to CWM, installed a stock ROM but now I'm stuck. I can't set up the phone without being able to touch the screen, can't add a bluetooth keyboard without touching, can't remotely control with ADB without touching (to confirm the request), and I can't remotely install anything because I haven't added my Google account yet (clean flash of stock ROM).

I've tried to Google this but have had no luck, do any of you guys know if there exists a flashable VNC or other remote software which I can just stick on the phone, and then be able to VNC straight in (without confirmation) to control the phone and get it set up?

I wanted to set up the phone as a desktop computer for the kids (MHL-HDMI for the monitor, bluetooth keyboard and mouse for control, speakers in the headphone jack for sound).

Thanks for reading my question guys and any ideas you may have!
My chronological life in Mobiles

Philips Savvy, Nokia 3310, Nokia 5510, LG U8120, Nokia N70, Nokia N73, SE C903, Nokia E61,
Palm Treo 750, Apple iPhone 3GS, HTC Trophy 7, LG Cookie T320, Huawei Ideos, Huawei Sonic,
SE Xperia Play, Samsung Jet, Samsung Galaxy W, HTC One X International, LG Nexus 4