@Gary Logue
As mentioned earlier, the first question is, do you need a novice program, like Starting strenght?
If you come back to training after already running a novice program, it is still a good alternative, but be aware that you will just run it faster and go over the linear progression very soon.
Second question is why it takes you that much time. For the main lifts, it is 5/3 with generous rest (say 5 minutes). Including 5 minutes of rest before going to the next lift, it will take you around 30 minutes. It is a novice program, so the weight is not that high in absolute.
The warmup does not add much time. Rest between warmups is almost as long as the time it takes to change the weight (it is a warmup, it should not take much energy). Maybe you are resting too long during your warmup or doing too much of it.
If you had success with Faleev 5x5, then go for it. Just alternate bench press and press if you want to have the press.
There is also the alternative of running Power to the people. At first, you do it 5 times a week with only bench press and deadlift, and after a while you add the squat and the press. There is a progression like that in the SFL manual, although I don't remember the specifics (and have no access to the manual at the moment). That would be my first choice. Short sessions, frequent practice.