Red light therapy LED spotlight
Yea, you can mount them on a circuit board just like everything else.
The Phillips LEDs you link are meant to be mounted on a circuit board that is well cooled (heatsink and/or fan) as these are high-power, specifically ~750mW for red. 

There are similar LEDs called Luxeon Rebel which look strikingly similar to those phillips ones which you can buy breakout boards that don't have any of them mounted already.  I believe they are sold by sparkfun.com

Since your application sounds like it is targeted at a specific area, the solution needs to be compact.  You'll need to design a circuit board and get it fabricated.  You'll need to be able to draw all the heat away from the board since you'll be keeping it on for 15 minutes.  This means a wicked heatsink and a beastly fan which mean this won't be the most silent device.