At 6 mins 30 approx this shows exactly what I envisaged building before I had even seen it...lol The start shows a cool looking machine that turns the balsa not sure how it all works though lol
You can easily get that smooth movement by using a similar idea to a shock absorber - don't worry it won't need to such tight tolerances inside.
Basically you would have a round weight running in a well fitted tube filler with oil. The round weight would have a hole in it so the oil could pass through . Depending how small the hole was it would give different rates of how fast the metal round weight falls in the oil filled tube. Now in basic form you would attach the weight with wire for instance that ran out and was mounted on a pulley above the frame it raises. Obviously wire would be the cheapest but you could use rods or chains to move the dipping frame.
Now pushing the frame down could be made lighter by (you will be overcoming the steel weight moving through the oil) incorporating a one way valve. Probably wouldn't need to worry about this TBH unless you had a huge weight.