There is no such thing as chlorine lock. What happens is that continued use of stabilized chlorine products, such as Trichlor tabs/pucks or Dichlor granular/powder, increases the Cyanuric Acid (CYA) level and that makes chlorine less effective unless you proportionately increase the Free Chlorine (FC) level to compensate. Algae starts to develop and this initially is seen as a hidden chlorine demand as chlorine gets used up faster than the tablet dissolves. Eventually, the water turns cloudy and then green (for green algae). At 80 ppm CYA, if your FC level got below 4 ppm then the chances get high for getting green algae if the pool has nutrients (phosphates and nitrates). For manually dosed pools, 6 ppm FC is the minimum target at 80 ppm CYA.
If you want to use only Trichlor as your source of chlorine, then you have to use a supplemental algaecide to prevent algae growth -- either weekly PolyQuat 60 or use of a phosphate remover (both are extra cost -- around $2-3 per week for your sized pool). Either that or you have to dilute your water enough to keep the CYA level lower. With Trichlor, for every 10 ppm FC that it adds, it also increases CYA by 6 ppm. With Dichlor, for every 10 ppm FC that it adds, it also increases CYA by 9 ppm. Unstabilized chlorine does not have CYA, but Cal-Hypo has calcium. With Cal-Hypo, for evey 10 ppm FC that it adds, it also increases Calcium Hardness (CH) by 7 ppm. The other alternative is to use chlorinating liquid and bleach (6% Clorox Regular unscented) which do not have calcium nor CYA, but you would need to add it every day or two unless you have an opaque-to-UV solar cover and even then would need to add chlorine about twice a week. There are automatic dosing systems for such liquid chlorine sources.
Unfortunately, there is no solid slow-dissolving source of chlorine that does not contain CYA. Lithium hypochlorite is a powder fairly concentrated in chlorine, but it is very expensive and it dissolves quickly. Dichlor contains CYA and dissolves quickly. Cal-Hypo, as mentioned above, does not have CYA though does have calcium and though it is usually granular it does come in pucks requiring a special feeder (NEVER put them into a Trichlor feeder), but they tend to break down too quickly and leave a messy residue.
It's not true that draining from the bottom removes more CYA because in most pools the circulation is good enough that the CYA is well dispersed. If you don't believe that, then invert a sample tube and put it down near the bottom, turn it over, then raise it out of the water and test such "bottom" water compared to water about a foot down from the surface -- you should find all the measurements are similar except possibly the FC level might be a little higher in the depths on a sunny day.
You are right that when Total Chlorine = Free Chlorine that this means that Combined Chlorine (CC) is zero and that's a good thing and a normal situation. CC is chlorine combined with other compounds, usually ammonia. When you measure any CC, it means that not enough chlorine is available to get rid of the ammonia (and urea) from your sweat (and urine). It's rare to see in a residential pool unless the bather load is high and the FC gets too low or the CYA level is very high (as these slows down the rate of elimination of CC). By the way, even though chlorine combines with CYA (which is why CYA makes chlorine much less effective) these "chlorinated cyanurates" measure as FC because chlorine is released from CYA relatively quickly (in seconds). However, it's the "active" or instantaneous chlorine (hypochlorous acid) concentration that determines the rate at which chlorine kills bacteria, inactivates viruses, kills or prevents algae growth, oxidizes swimsuits and hair, etc. and that active chlorine concentration is roughly proportional to the FC/CYA ratio.
Take charge of your pool and learn more at the Pool School at Trouble Free Pool (including the article on defeating algae). The first step is getting a good test kit. The Taylor K-2005 isn't bad, but the Taylor K-2006 is better or the TF100 from tftestkits(dot)com. You can just get the FAS-DPD chlorine test here
since that will give you the equivalent of the K-2006 given what you already have -- this FAS-DPD chlorine test measures Free Chlorine (FC) and Combined Chlorine (CC) with 0.2 ppm resolution (using a 25 ml sample; 0.5 ppm resolution using a 10 ml sample) and the test does not bleach out at high FC levels so can measure up to 50 ppm (useful when shocking a pool).