To my understanding Lamina and thermal lag engine are both the same type. Thermo-acoustic is something different. Actually there are no videos of thermo-acoustic engines in YouTube. All are Lamina/Thermal lag type, but some builders or sellers prefer to call their engines thermo-acoustic, just because the name sounds more scientifically or can be sold better. There is indeed very close visual similarities to a kit sold as acoustic laser, where perhaps the confusion comes from. Lamina is able to run in a free piston mode too (without flywheel). This fact makes some believing that a resonance of acoustic waves is what moves the piston. Actually the resonance is defined only by the piston mass and the air spring and the frequency is much lower than the natural resonance frequency of a test tube with this size.
Anyway, the biggest difference between horizontal and vertical Lamina is the place where you apply the heat. The best is to apply the flame just on the border steel wool / air. In a vertical Lamina the flame is applied on the bottom of the test tube, which is the other end of the steel wool. In this way much less heat reaches the right place and Lamina is much less efficient. One way to enable Lamina working at lower temperatures is reducing the compression ratio. I would try shorter test tube (to bring both regenerator ends closer) with larger diameter (to reduce the compression). Shorter piston stroke and reduced opening of the orifice may also help. Keep in mind that Lamina will work with less rpm and less power, so you have to pay special attention to minimize all frictions.
I am currently playing with measuring the shaft power of my Lamina. It could reach almost 200mW for short moment and then the cold side gets warm and the power goes down to around (130-140)mW. From this I was able to extract maximum 80mW of electrical power (8V @ 10mA). This is enough to light 3 white super bright LEDs. I think it can even power a pocket radio.
Unfortunately Lamina is a desperately inefficient engine. Assuming that a small alcohol burner delivers ~40W (if not even more) and the top power of Lamina is 0.2W, we get only 0.5% efficiency, which is quite discouraging result. Despite the facts, Lamina remains the most simple power producing engine.
) Try it and see. Make sure you take pictures. 
