How to simplify a multiplicator that currently consists of many adders?
If speed isn't a concern, you could use an accumulator and repeatedly shift and add the multiplicand to the accumulator rather than use parallel multiplication. It should at most take 8 clock cycles, but if that's too many, you can cut that down by using a 2bit x 2bit or 4bit x 4bit parallel multiplier in conjunction with the accumulator.

Here's a Logisim circuit of an 8-bit multiplier that shifts and adds 8 times to find the product of two 8-bit inputs. It just calculated 5 * 6 to be 30