Solution
The solution is to use different PFI lines for the frequency inputs. The default Source terminals documented in the TIO Physical Channels result an internal routing conflict when trying to use all 8 counters for Frequency measurement, while the Gate defaults work fine.
The Low Frequency with 1 Counter measurement method requires the requested CI.Freq.Term signal to route to the Gate input of the counter internally. TIO Signal Connections for Counters, you can see that the default channels for Low Frequency with One Counter are: PFI 38; PFI 34; PFI 30; PFI 26; PFI 22; PFI 18; PFI 14; PFI 10 (Gates Sources).
The Default Gate terminals defined by software can route directly to the counter Gate terminal. However, if you pick any other PFI pin, it has to go through an indirect path to get to the counter Gate input. Since these internal lines have restricted connectivity, conflicts occur when multiple non-default terminals are used, leading to routing resource exhaustion. This is why the default Source Terminals create a conflict that runs out of internal route lines.