Can you tell us what a typical hunt for you is? Just walk me though it. The thing is they're tough to hunt, thats just a given. Its your first year so you've just began to learn what to do. Remember that slow movements are key because at this stage in the game there are few to no leaves left on the trees so they'll be more apt to see you coming. Get to your spot and wait. If squirrels are in the area then you will move often than not get your shot after sitting for a while. Be patient. Stay with your 22lr(try for a shorter shot). Its quieter and from what you are saying on ranges it or a 17hmr is the way to go. If you have access to a 17 that would be the way I would go if 70 yards is really your average shot.
One other thing I can suggest to you is on practicing you're shots. Now bear in mind I have no clue how and if you practice. I would definately zero in at around 35 or 40 yards. I'd then see how the gun hits at around 15-20 yards and then also at 60-70 yards. You'll learn how you need to adjust. I'm hoping that when you practice shooting that you are not just shooting at a paper target nailed or taped to a board. If you are then I suggest taking 2 or 3 of 20oz coke (or some other bottle with a label that you can clearly see). the trick is to shoot the label of a bottle and readjust on the next bottle as quickly as possible shoot and continue as fast as you can accurately shoot. The point is to teach you to look for the impact if you miss and adjust your aiming. I've shot competition in rifle, pistol, and shotgun time trials and this is the best way I've learned to practice.
Lastly, you're obviously picking and choosing your shots as any good hunter should do but you may be choosing to cautious of shots. Many times from the ranges you're describing you can shoot and if you do miss the squirrel will not realize where you are and will look right away for something out of the ordinary orrun off and comeback in the next few minutes to scope things out and find out what the heck just happened. So when you do miss stay still and wait for that other shot. If you are moving around he will see you and he will bolt.
On the topic of using a 16 or 20 or 12 gauge shotgun, they're great at the right time of the season. In the early part of the season when the leaves will break up your outline and you can get close they're great. But they're noisy as all heck and will scare other squirrels out of the area.