With model 66, like most of the narrow footed straight stitchers, it's very easy to guide the fabric for perfectly straight seams, and both curvy and angular turns are done with ease. This is one of their advatages and it makes them a joy to work on. You do have to guide the fabric with you hand every so slighly and you can't sew completely "hands free". Your test stitching looks good though. If you have checked the feed dogs and made sure they move in a straight line 180 degrees on the fabric it's adjusted fine. Do the test with a ruler if needed. Also make sure the teeth lay flat, as close it gets to a perfectly horizontal plain. Do this by eye, and the check with a flat ruler on all four sides (or flat piece of other material ). The natural movement of the feed dogs is cirular, as I'm sure you already have figured out. Feed dogs can in theory be worn or damaged, but usually not, even on machines that have seen a lot of use they are tend to be all fine. It's worth checking the state of the teeth.
Don't give up on fine tuning your machine, if you have messed a lot with it, it might need a "full service".
Here is a link to a simple service manual. If a part isn't obviously out of sync I wouldn't fiddle with it. I don't know what condition your machine was in when you got it, but usually they get better after a period of regular use and maintanance (extra tentatively and frequently oiled and cleaned for a period). The advice can seem a bit over the top, but if there were signs of rust or lots of grime, it will take a bit for it all to be flushed out. Rust will gradually dissolve as the machine is used, depeding on what type of oil and fluids you have cleaned with. The oiling part is repeated ad nauseam, but it's almost impossible to be to tentative in a run-in period.
Model 66 does perfect stitches, it's a nice model. I think you might have ever so slight tension imbalance on the stitching test. When balanced the stiches should form a perfect line of arrow straight stitches. I'm being very fuzzy now, but when you have the interlocking of upper and lower thread happening in the two pieces of fabric, they will hardly show. You are doing all correct, test sewing with two layers of light cotton.