Hi there!
1) Transplanting alone will not necessarily increase the size of your plants. Additionally, it usually isn't the most important factor in growth rate. Appropriate temperatures, daylength, and watering have a much bigger impact. If you optimize those conditions, you can also begin using fertilizers to great effect.
2) The leaf size of most mexican Pings
will increase if you provide them with less sun. The leaves will also get thinner. In too little light they become sickly, elongated, prone to infection, and unable to produce dew and digest prey. It will also become slightly more difficult to ensure that they dry out between waterings, and IMO shade increases the potential for rot. Pings in general dislike heat, but can handle lots of light provided they simultaneously get cool (no hotter than 85F) temperatures. This can be a tough balance to achieve, and I have zero chance of doing so here during Georgia summers.
3) For Pings a mix of sand
erlite is excellent, and I also use Turface with good success. I got lots of rot when I tried adding long fiber sphagnum or peat to my mix--I am in the humid, rainy south, but if you lived out west I imagine you could get away with this. They can be liquid fertilized at 1/2-1 tsp per gallon of most liquid feeds and will increase in size, greenness, and offset more readily. A pinch of limestone every month or so is very beneficial, since most grow in limestone soils. In the winter they need almost complete dryness (I water perhaps weekly or biweekly, always with a spray bottle and only wetting the top 1/2" of media... I also have then in a shallow bonsai pot), and also need a shorter (~8-10 hours) photoperiod and cool temperatures (40-60F) for their dormancy.
4) For most South African Drosera, changing the media doesn't really impact growth rate unless they're being smothered by weeds, moss, or algae. Or if you're having a problem with root rot or fungus gnats. Things that will more directly impact their rate of growth (and thereby size) include: lighting (bright as possible, especially if indoors), photoperiod (12-14 hours), temperature (50-85F; most dislike heat above this and grow slowly or burn), and foliar feeding weekly with sprays of ~1/4 tsp/gal of liquid fertilizer.
Hope this helps! Good luck.