In which I attempt to show through math that the proposed rocket in #1 doesn't do the job of getting to orbit. This was mainly for my own interest--I don't really expect it to change the OP's mind. But hey, math and spreadsheets--it's like candy for an engineer.
Starting with some extremely rash assumptions (never make assumptions about rashes!):
0.5 kg payload
0.5 kg nose cone, roll control system, and guidance computer
0.8 mass fraction for motors
Thrust vector control mass 0.5kg for Stage 4, 1 kg for Stage 3, 2 kg for Stages 1 & 2
ISP ~225s (matches the CTI O8000)
Thrust is constant, propellant mass burn rate is constant (this mainly just makes the math easier)
Note that these assumptions are extremely optimistic. I would be absolutely shocked if they are possible except possibly increasing the specific impulse.
My process was to work backwards. When Stage 4 burns out, you want to have reached 7800 m/s. You enter the propellant mass and the impulse (plus an assumed time, which doesn't really matter), you get starting and ending acceleration based on your loaded and burned out mass, you integrate the acceleration, and you get delta V. That gets you your desired starting velocity to reach that ending velocity. Then you wash, rinse, repeat with each stage below. The end result is the rocket you would have to loft to ~200 km, turn horizontal, and start firing to make it to orbit.
So here's how that shakes out:
Stage 4: Full O motor, 41000 N-s, delta V 1850 m/s
Stage 3: Full Q motor, 160000 N-s, delta V 2500 m/s
Stage 2: Full S motor, 640000 N-s, delta V 2300 m/s
Stage 1: 50% V motor, 890000 N-s, delta V 1150 m/s
The astute reader will notice that you need to loft 1730 kN-s worth of impulse to orbital altitude just to get from "standstill at that altitude" to "orbit at that altitude". That whole stack weighs just a hair over 1000 kg, so it seems fairly plausible given the mass and payload capacity of the Lambda 4S. Also note that this is far, far beyond the capabilities of any amateur rocket builder.
QED.