"eat the tastiest food first no matter where it is in the bin" ..... Yep, that's what I found out.
IMHO it is better to feed slow so the worms finished off what's there before adding new goodies. That's why I've set up a "holding/pre-rot" box. Some people commented that there is no difference whether the food start to rot in the bin or outside it but I beg to differ.
By having the pre-rot box I added time for the worms to keep working on the old stuff. And I (or the worms?) eliminate the waiting time for decomp. to start in the bin.
By adding to the bin, the worms will neglect the old "food" and move on to the new stuff, and I ended up with a bin full of half processed matter.

It seems to me that there are three basic approaches to handling a flow through bin.

1) You can prep the food up front, as otis11 suggests, or

2) you can finish the castings by having a curing bin at the end, as equinoxequinox suggests, or

3) you can do the traditional wait for 3.5 months for VC at the bottom of the FT bin so that most of the cocoons are hatched, the bottom is dry and the babies have migrated up before harvesting.

There are problems and advantages to each method. The first two will give you better quality VC, I assume, and more pure castings.
The last one would give your an end product that is more like fine leaf mold textured compost, at least in my bin. I guess it just depends on what you are using the VC for, and what you want from the worms.

For me, at this point I am leaning toward the curing bin part, since I want lots of VC pretty quickly, but am still new enough that the thought of 'wasting' worms and cocoons by missing some is almost painful. I can understand those who like to pre-rot, but I am not in that place right now. I imagine next year I will be swimming in both worms and VC, so I will be waiting and just getting out medium-grade VC from the bottom of the bin and using it directly on the garden with a minimum of fuss and sorting.