So you have a quilt to make how do you speed up the piecing process. The best way I know is to work like a process worker and tackle one process at a time. Add to this chain piecing whenever possible. By continuing to do the one task at a time you are speeding up the process as you get into a rhythm and in no time you will have that process completing for the whole quilt.
When chain piecing half square bocks or hourglass blocks I will do a say 10 or 20. Go through one side of the drawn line and then turn the whole chain around and repeat on the other side of the drawn line. I then cut all the threads between the units and slice through the joined line and press them. I have my iron and cutting board set away from the sewing machine that way I get up and have a bit of a break which helps stops boredom setting in.
Even when I join blocks especially nine patches I chain the units in such a way that the chain acts like a pin to keep all the units together.
For a nine patch I would have piles of the nine units at the edge of my sewing machine. Stitch the first and second units from each of the 3 rows, stop. Do not cut the threads at this stage and do not press. Then stitch the third unit to the second unit of each of the 3 rows. Keeping all the threads attached. Continue in this way for each block, when they are all done or you have a reasonable pile take them to the ironing board.
The joined threads act as pins and helps to keep the block accurate so your seams meet. Press the seam allowance and it is really easy see how to press the seam allowance alternating so that they will nest when you are putting them together.
Stitch your rows together on each block, as all the pieces for each block are still joined you can chain all your blocks as you stitch as well.