Solder third hand with screw mount base

Get a "PV Jr" and the tray base.
The PV Jr. is very versatile, genuinely useful.
The tray base is about 8 inches or so diameter, won't tip, stays put, and it has rubber feet.

http://www.panaviseonline.com/Panavise_Jr_Model_201_p/pv-201.htm
http://www.panaviseonline.com/Panavise_Parts_Tray_Base_Model_312_p/pv-312.htm