TLC5940's Big Brother: TLC5955 48-Ch, 16-Bit, PWM LED Driver w/DC,BC,Open-Short

No, I should try using flux. Are those flux pens any good? Do you use an artist's paint brush with the liquid flux?

I need to get myself a temp controlled iron and a selection of bits.

Why did you chose the tlc chip for your project? I would have used 6 x max7219. Do you need 16 bit brightness control of every dot?