First, Beer's Law always fails at high concentrations. Your experimental results are consistent with this. Second, even great spectrophotometers costing tens of thousands of dollars struggle measuring accurate absorbances over OD values of 2, even though they claim to be good in some cases up to values of 5. An inexpensive one could struggle with OD values over 1. Even if they say it'll read 0-2, that doesn't mean it will read high values well - just that it'll return a number. Regardless of your instrument, you should almost never make a measurement with a value over 1. Quantum yield and extinction coefficient measurements are almost always done with OD value under 0.5, and frankly I don't trust them unless they are < 0.1. So any lack of agreement between theoretical and experimental absorbance values above OD = 1 are going to be suspect anyway. You are also seeing lack of agreement with low OD values. This is most likely due to either (a) inaccurate concentrations, (b) inaccurate extinction coefficient, (c) instrument calibration (both wavelength and intensity). Since (c) is what you're kind of trying to do, let's forget about that one for a second.
Thinking about (b), here's some things to keep in mind. The molar extinction coefficient is wavelength, solvent, and concentration dependent. They're also notoriously hard to measure well, and there are a lot of bad extinction coefficient values out there. Make sure you have a good one by checking around literature sources to see if the value you use is consistent with a lot of different reported values. (Also check and make sure you are using the same solvent the literature value was measured in, and make sure also that your solvent is good. For non-aqueous measurements, wet solvent can lead to big shifts in wavelength/intensity values, and impurities can lead to background absorption.)
Are your cuvettes good quality? If not, you could have light losses from your glass/plastic. (see additional note below)
I also suggest checking the linearity of your instrument by doing serial 20% dilutions starting with an OD approximately 1 and checking to make sure you get a nice line. This will give you an idea of whether your instrument is behaving well, irrespective of quantitative accuracy of a single point.
Regarding (a) - making accurate solutions is harder than most people think. But assuming you are making them well, some other things to consider: Where are you buying your dyes? If they are old or from poor quality sources, the effective concentration can be a lot lower than you think it will be. Trying your expt with a few different chromophores can help you determine if you've got a bad batch of one.
EDIT: I didn't check your actual numbers... but I noticed after reading again you said your path length is 1.2 cm and your cuvette is "test tube style". This would mean the cuvette is round, yes, with a diameter = 1.2 cm? Is the spectrometer specifically designed for a round cuvette? If the cuvette is round, keep in mind the actual pathlength won't be 1.2 unless the beam is really narrow. The beam will be experiencing all kinds of different path lengths, most of them less than 1.2 cm, depending on where individual photons cross through the sample. This will make it really hard to apply Beer's Law, and your measured concentrations will probably be less than theoretical based on a path length of 1.2 cm. Plus you'll have all kinds of weird reflections could interfere with the measurement. There's a reason people use square cuvettes. If you're using a round tube as a cuvette, I strongly suggest you change to a square one, as this could be a significant portion of your problem. If you don't want to invest in quartz cuvettes, inexpensive plastic ones perform reasonably well for aqueous solutions in the visible region.