Sub Panel for Floating Boathouse/Dock
12/2 is awfully, awfully light for a 300 foot run.  It's not a bad installation, and it's legal and safe to breaker that 20A.  It just won't be very satisfying if you try to run a heavy draw appliance.  As things are, your tiny 60W / 0.5 amp load won't be a probem.  Punch your actual amp load into a voltage drop calculator (and specify 99% allowable voltage drop) to see what the voltage drop will be. 

You new setup will delete the GFCI receptacle, but that's a good thing. The problem with GFCI's at beachside is that if the GFCI itself gets wet, electricity can leak from the unprotected line side of the GFCI and kill you.  A better place for the GFCI is actually as a breaker in the main service panel, so the entire wiring run and the panel and the receptacle are all protected. 

Since this is only one circuit, all you need here is a shutoff switch, provided you have a GFCI back at the main panel.  This can be a $19 fuseless shutoff switch, or a $20 2-space subpanel with a $5 breaker installed in it (using the breaker as shutoff switch). Guests need to be able to shut off power FAST if needed, so get a panel where the main breaker is obvious, not hidden among the other breaker(s).   

If you want the GFCI at beachside, figure on a $65 hot tub subpanel which has a GFCI "main breaker".  

GFCI breakers for your main panel are $40, so this is a wash costwise.  If you do have that, you will not need any GFCI devices beachside, and you can satisfy GFCI requirements with a sticker that says "GFCI Protected". 

Using SJOOW cord between the flexing sections is correct. 

If you're actually using the conduit wiring method where all boxes are connected by continuous conduit, 12/2 UF is a very tight fit in 1/2" conduit and a miserable pull (some manufacturer's UF are actually too big!)  THWN-2 individual wires are the right thing for conduit, and you get to use stranded wire, which is a joy to work with.  Only downside, you'll need 3 colors of wire.

If the conduit location is exposed to direct sun, PVC will take UV damage inside 3-4 years (so paint it).  Sched 40 PVC also won't hold up to physical damage (so use Sched 80 or EMT at sensitive areas).