I would  epoxy some plywood pads, use 1/2" plywood, under the deck and then screw pad eyes to them with screws that do not go through the deck Then run the bungee cord through the pad eyes.

If you were to but the paddle float and pump in a deck bag and then mount the pad eyes to mount the bag under the deck You might be able to mount the pad eyes to the sides of the kayak just under the deck.

Here is the bungee-under-deck arrangement I did on my Shearwater Sport. Certainly easier to do when done while the deck is not yet glued to the hull. I am happy with how this works.

That way I felt comfortable doing without the bungees on the deck.

   I'd build some soft loops- small rope loops potted in small disks of ply, glued to the under-deck, then thread your bungee pattern through the loops.

I am winding up a build and i built a bunch of tabs for various inside-the-hull hold-downs.  picture below, middle right side of the picture you will see this upside down u tab that creates a hold down point.

i created these simply by taking a with a pen with a diameter i liked, and taping it to a board with duct tape.  (epoxy releases very easily from the non-sticky side of duct tape).  i then wet out four strips of 3 inch glass tape about 6 inches long and glassed it over the duct tape pen on the board (which formed a male mold).  i added some graphite becuase i wanted the piece to be black.  i then put some saran wrap over it and used two boards to push the tape down tight around the 'pen mold' (see below)

once this cured, i then had a 6 inch by 3 inch piece with a channel down the middle.  i used a band saw to trim these into finsihed tabs (each tab is about a 1/4 inch wide so the whole piece made about 20 tabs). 

i then glued the hold down tabs directly to places inside the hull where i was going to want bungee holds down.  i glued it with epoxy thickened with cabosil.....and these anchor points are very strong.    that said, the inside of my hull is glassed.  if it was not glassed, i might put a glass patch down first on the wood and then glue the tab to the hull over the patch.

these are very light, unobtrusive and strong and have been very useful for me.

howard

   How much space is behind the seat? 

Grumpy - Inside the cockpit there is 2-3" behind the seat.  Enough for the paddle float but not for the pump.  I usually keep the float on the rear deck, just behind the seat, in the bungees I use for paddlefloat rescues.  I keep the pump on the forward deck.  But neither of those places is ideal if I am practicing self reccues or T-rescues.  Its probably better to keep as much as possible off the deck.

   As an example on the building supplies section a carbon fiber eye-strap for holding bungees that is glued on. It could be installed to the under deck. At $10 each it might just be an idea worth adapting. You could also do the thru-bolt eye strap or fabric tab, with short screws and an acorn nut. I'd put pan head or flush head on outside and acorn inside cause my knees never get up there. Acorn nut might bruse but not cut like threaded screw end. 

Interestingly the pump on the outside under bungees is the standard here in Florida for guides and experienced paddlers.  

   For my wife's Wood Duck 12 I installed an underdeck bungee for pump and throw line.  Works great!

I just used 4" pieces of webbing, folded in half.  Wetted out the open end with unthickened epoxy, then set it in a small bed of thickened epoxy.  I taped the closed end with painter's tape to keep it dry.  Once cured, you have a flexible webbing loop to run a bungee through.