How to drive 400W of High-Powered LED's in parallel / series?
There are many drivers.  Not so many that will power 20 in a string. Many you  can expand the voltage to what ever by using an extra MOSFET.

The 14 Cree must be Red probably XPE wich are typical 2.4 at 700mA. I have found XPE to be about just under 2.0 Volts at 500mA.   

You will need massive thermal management to run them at 700mA.  

20 is pushing it.  I went with 16 max but that is for all colors. 20 Red would squeak by. To be compliant with Electrical Saftey I keep voltages at 48 max.  

You approach depends on how any you are going to make.  Is it  a 1-2 or are you going into production?

Running LEDs in parallel is not acceptable to me.  There are those that can argue that point but they would be wrong. Been there done that. It will work only if the LEDs are running at ambient temperatures which is not the case here. 

I just got in a TI Eval Board for the LM3466 load balancing circuit. It appears to be the way to go with parallel strings when the current is constant and they are not dimmed. 

You can build a very efficient DC-DC driver for $2-3.

I would power your circuit with more than 12V for efficiency and cost. A boost driver will cost more than a buck step down driver and be a little less efficient unless you spend more. 

I'm not a big fan of COB arrays. Too much heat in too small an area. You will need very good thermal management to pump them at 70 Watts.  Chilled liquid cooling would do it.

If you are just making one or two use constant current poser supplies.  The Meanwell HLG series would do very well here.  One supply for each string unless you use a load balancer for multiple strings. 40 @ $30, 100W @ $47.