Which radiant setup would work better?

I've got a system installed now setup like the first diagram in the attached. It works, but my impression is flow is not consistent and it is a bear to get the air out at the beginning of the season. The manifolds use a compression ring and o-ring to make the connection to pex...I think one of the o-rings got damaged and that is where the air is getting into the system. I'll play with that during the summer when things warm up.

But, I'm wondering if there'd be much of any difference in performance if the pump location was changed. Thoughts? Recommendations?

I would believe the pump should be between the boiler and the tempering valve.

Do all of the loops come on when heat is required or does each loop have a thermostat and control valve? If they are all on a single control, I suspect a pressure bypass is not needed. If the flow rate supported by the pump is a lot more than what the loops need, a bypass couldn't hurt. Easier on the pump. I think I would use the bypass only if I needed to control flow rate in individually controlled loops. It has the effect of making the system a constant pressure to the loops. I am not a contractor.