One light switch powers two separate light switches
Go for the Pro model

I spoke with Lutron's tech support online via livechat and the Lutron Pico remotes do support being paired with more than one Maestro or Caseta dimmer.  With the correct parts, you also can leave the mechanical switch in place upstairs to allow a houseguest or first responder quick control of the lights.

You'll need a black pigtail (match the existing wire gauge) and a few more wirenuts for this, as well as two Lutron PD-10NXD (this is the pro model, which adds the hardwired switch support) dimmers and a Pico remote with a wall mounting kit.


Turn off power at the breaker (if it isn't already off that is)


In the upstairs box:


Remove the two black wires from the old switch and nut them together with the black pigtail.
Attach the other end of the black pigtail to the black screw on the upstairs switch. (This effectively uses the 3-way switch as a single pole switch.)


In the downstairs box:


Remove the top (in your photo) black wire from the left 3-way switch.  Nut it to the red wire on the dimmer that's going in the left side.
Remove the top (in your photo) black wire from the right 3-way switch.  Nut it to the red wire on the dimmer that's going in the right side.
Pull out the neutral bundle from the bottom box. Connect the white wires from both dimmers to it.  (This will yield improved dimming performance and avoid flickering or other misbehavior if CFLs or LEDs are installed.)
Remove the bottom (in your photo) black wire from the right 3-way switch. Nut it to the black wires from both dimmers.
Remove the red wire from the right 3-way switch.  Nut it to the blue wires from both dimmers.
Pull out the ground bundle (if present) and nut the green wires from both dimmers to it.  If no grounding means is present in the box, nut the green wires to each other but do not connect them to any other wires in the box.


Back at the upstairs box:


Install the Pico remote and wall mounting means adjacent to the upstairs switch box.
Button both boxes up.
Turn the power back on at the breaker.
Pair the Pico remote with both Caseta dimmers as per the supplied instructions.