Yes, you have run out of available tuners on your SWM8. However, the swap for a SWM16 is not just a plug and play. A SWM16 is really like 2 SWM8s in one unit. Each output of the SWM16 can support upto 8 tuners. So, in addition to swapping the switches, you'll also need to connect the HR34 to a different port on the SWM16 than your older receivers.
IOW...
SWM16 SWM port 1 >>>> 2 way or 4 way splitter >>>> HR24 & HR20 (4 tuners)
SWM16 SWM port 2 >>>>>>>>>>>>>>>>>>>>>>> HR34 (5 tuners)
There are other ways of doing it, like HR34 and HR20 on one port (7 tuners) and the HR24 (2 tuners) on the other, but you get the idea. You can't have more than 8 tuners on each leg of the SWM16.
IOW...
SWM16 SWM port 1 >>>> 2 way or 4 way splitter >>>> HR24 & HR20 (4 tuners)
SWM16 SWM port 2 >>>>>>>>>>>>>>>>>>>>>>> HR34 (5 tuners)
There are other ways of doing it, like HR34 and HR20 on one port (7 tuners) and the HR24 (2 tuners) on the other, but you get the idea. You can't have more than 8 tuners on each leg of the SWM16.