You can actually do all of those movements (except pull down) with dumbbells, which offer a minimum of 'setup' and don't require a spotter. You may even be able to find a dumbbell rack outside of the 'heavy weights' area, depending on your gym.
Goblet squats are an easy modification with dumbbells or kettlebells. Bodyweight squats are still great for flexibility and form - you can do them into high rep sets (eg. 20-30 no pause) for endurance work as well.
Keep on with the body weight lunges until you can do them without falling over - keeping yourself stable is one of the reasons they are so hard to do.
Depending on your goals, you probably don't need to use the leg press if you're also squatting.
And you can alternate pull downs with a pull-up assistance machine as well, just to give you some options to switch around with during busy gym hours.
My gym gets busy at about 7/7:30 until 10:30, it's a popular 'before work' time. I resigned myself to an early start to the day *eurgh*, but you may find it a bit quieter in the 11-12 time slot: in between the morning and lunch rushes. Also, headphones and workout music go a long way to helping ignore people around you.