MAXSA Innovations (47332) solar deck LED light systems.

You can find them in 4 packs for less than $30.00 if you look around.

They are L shaped and when mounted to a rail the Solar panel sits on top of the rail and the light shines down. With them they do not blind people and are also good for using on steps or even around the edge of the deck "flooring".

Two screws are all that is needed to mount them.

I wouldnt bother. I have the same situation. What i did was to go with stainless steel leds and put them in the risers on the steps and in the floor. Also you can get the solar lights that attach to the side of the 4x4 which will look better imo than trying to adjust the structure just to put solar caps on.

Have a look at these http://www.amazon.com/Brown-Round-Solar-Fence-Lights/dp/B00KYXT3FG/ref=sr_1_6?ie=UTF8&qid=1408633730&sr=8-6&keywords=deck+lights

http://www.amazon.com/Stainless-Steel-White-Lights--Included/dp/B00DL4U19W/ref=sr_1_2?ie=UTF8&qid=undefined&sr=8-2&keywords=deck+lights+stainless

less work and i think a better look.

Sorry didnt see that you already used the lights that attached to the side, not sure if they were this brand though. If you read the reviews for the solar caps they last even less !