Another thing about squatting, it's the idea of needing (more) flexibility. While it sounds logical, strength supersedes flexibility when it comes to motion. Take stretching for example. It may make us more flexible, but in fact it also makes us weaker. On the other hand, growing stronger gives more stability of the joints thereby making motion more stable as well, even if it has little to no effect on flexibility itself. On the third hand, being stronger allows a more full range of motion, or existing range of motion, which could be perceived as greater flexibility when compared to feeling some pain at either end of said motion. Personally, I seriously considered either option when I started playing golf and I found I played better (and could practice and play longer, all day long in fact) when I stretched less, not even a little bit before a round, I just went straight to practice or the first hole and swung away. In the gym, (after some experimentation with various lifts and motions) I ended up doing a single motion (called a pull clean, a practice lift for the Olympic lift clean and jerk) but with a very heavy weight, just to get stronger and maintain strength. This greater strength, I could have used it to its full extent to hit the ball farther for example. Instead, I used this to reduce the effort I put in, and to focus on best precision, because golf isn't a game of how far, it's a game of how close. The point for our purpose is that strength allows lower effort for same power output, and allows fuller range of (existing potential) motion.

Also, the standard method to grow stronger is basically to repeat specific motions. That's just called practice, and the motions we practice, we become better at it on top of growing stronger. Technically it's called neuro-muscular, but it could just be called skill. In effect, greater skill allows more precise motion which translates into greater power output, i.e. greater apparent strength independently of muscle size. Also also, it's possible to practice partial motions and progress gradually to the full motion. So for our purpose, a squat can be done half-way for a while, we'll grow stronger and more skilled at the same time. Eventually we'll be able to perform a full squat with little effort. Some lifters use a chair to sit at the bottom of a half-squat, so that's an option. Another option is to grab something (a door frame or something) to help us back up. In my research with toilets, I found the Japanese use what they call a grunt bar in conjunction with a squat toilet. Basically they grab it as they squat to crap. Anyways, plumbing shops sell all kinds of bars for showers, so stick it somewhere solid and that's your squat spot.

For the lift we call a squat, there's the back squat with the bar behind the neck and the front squat with the bar in front on the shoulders. The most difficult is the front squat, which means it must be done with a lighter weight. This is a good thing for a few reasons. We can dump the bar easily in case of lift failure, it's much safer than the back squat for this. It forces to straighten the back much more just to keep the bar on the shoulders, so it's safer due to a straighter back and it strengthens the back a bit more. It's a lighter weight so overall effort is less in spite of actually being more technically difficult due to the difficulty in keeping the bar on the shoulders through the motion.

Then there's the thing called cross-training, where we practice one motion, and the skill and strength gained with it transfers almost directly to another motion. So, in my experience, that single lift I did in the gym transferred pretty much directly to the actual motion I did playing golf - the golf swing. It also transferred somewhat directly to another motion I did often playing golf - a squat to tee the ball and whatnots. This is due to strengthening the back and the legs with that lift in the gym. The point is this means it's possible to eventually be able to perform a full squat, by gaining strength and skill with a different but perhaps easier motion at first. So that's yet another option.

-edit- It just occurred to me. It's totally possible to squat while laying on your back. Just pull your feet to your butt, repeat.