Mani.s just about your conical pendulum, I feel your apprehensions about swinging it by hand are pretty unnecessary as you can get it to be both very accurate and valid, you just have to be smart about how you go about it. Depth studies aren't about making things complex, they are just about explaining physics well, so best to keep it simple.
I would suggest changing radius, which is probably the easiest way to go about doing the experiment. For a specific radius (can then change radius to use as independent variable) I would recommend hollowing a pen and passing a string through, which gives you a nice handle to hold. Start spinning above your head (making the plane of revolution horizontal) at such a speed that you keep that marked length at the tip of the pen and get someone to film you as you keep that orbital radius constant (If you fail to keep it constant for a run you can just discard that value), the experiment can be made very accurate if you keep it at the one radius for 10-20 revolutions, so that when looking back through the footage you can find the average orbital period for each revolution (which should be the same anyway if your radius is kept constant).
If you are keeping your radius constant, then the mass on the string isn't moving up and down and isn't accelerating which enables you to equate centripetal (mv^2/r) and weight (mg) and them from their determine your relationship between force and orbital radius.
As for validity, the only thing that isn't valid about this method would be the friction of the tip of the pen hole and the string and if you are spinning ensuring that you keep it flat. Also just with depth studies, it isn't necessarily about making the most accurate or most valid experiment anyway, as long as you can identify the sources of error and their impact. Just another thing, never try and make your depth study too complex, much better to do something simple very well than fail to comment on everything for example I wrote 4500 words on launching a marble at different angles, and someone in the previous year got full marks for dropping masses at 1m, 2m and 3m heights which goes to show you can tease words out of anything so do something simple so that you can really get across the actual physics.