It might not be the TT it might also be a too wide bar for his build.In your pics,your elbows are down and tucked WAY in.Thats horrible riding position.
Try getting them up and more of a moto position.
You're leaning back because you're on flats,that's just how you have to ride them to keep your feet on the pedals and keep them from bouncing off.
Have you tried clips with like the minnar shoe or something equivalent ?Cuz if you tried them with an xc type shoe,it's really floaty and unstable feeling.
It's seems that you're trying to adopt a flat pedal riding style to a clipped in riding style without making the change.
I think your tt IS to short and you might be tucking your elbows under to prevent your COG from going over the bars.A longer frame and being clipped allows you to spread out bit more,lower your cog and maintain a more centered,aggressive position on the bike.I kinda did this transformation over the last couple years.
My big thing was finding a shoe( believe it or not) that made me feel confident in making the switch.I run the Minnars and spds with the tension all the way off so it's easier to release and I've yet to accidentally pop out because of low tension.