As S. Mcgrew stated, consider this as an imaging problem. If you collimate with an f=50 lens, and focus that with a f=100 mm lens, the nominal magnification is 2 (well, -2 if you were keeping track of signs). Hence a 1 mm aperture is imaged to a 2 mm image size. Some aberrations will increase that slightly.
If you increase focal length of the first lens to 75 mm, the magnication is now -(100/75) = 1.3, so the image will be 1.3 mm in diameter. (As images get smaller, aberrations may be a proportionately larger share of the actual spot size).
One warning - you state the 1 mm aperture is 2 cm in front of the LED. This means that only light that goes through the apertures is already traveling close to the axis joining the LED and the aperture. Most people would change this: they would put the LED right up to the aperture. If you do this, you will definitely get more light through the aperture. The configuration of your imaging lenses (focal lengths, distances, and apertures) will determine how much of that light gets to the image plane.
Second warning - you can't have a long distance between the two lenses, depending on their aperture. That will lead to vignetting.
The irradiance (power per unit area) at the image plane may not go up even if the spot gets smaller, it depends on how everything is set up (including lens apertures).