Concept of combining multiple FIR Filters into 1 FIR filter
What you tried to do in your example is combine the filters in series rather than parallel.
That is, if your signal is $$y = ((x*h_1)*h_2)\ldots*h_7$$ then, according to the associativity property of the Convolution, $$y=x*\underset{H}{\underbrace{(h_1*h_2\ldots*h_7)}}$$

However, if you wish to perform a parallel filtering then your signal is $$y=\sum_{i=1}^7 x*h_i$$
and acording to the distributivity property of the Convolution, $$y=x*\underset{H}{\underbrace{\sum_{i=1}^7 h_i}}$$