One way to consider this is to view the modern, high bypass ratio fan engine as nothing more than a large, fixed pitch, ducted turboprop. Some of them even sound like one. As the linked document pointed out, 75 to 80% of the thrust comes from fan air. The total thrust output is somewhat parallel to the turboprop manufacturer citing an "equivalent" horsepower based on shaft horsepower plus the small amount of tailpipe thrust.
That said, EPR is only measuring the core efficiency, unless it is an integrated system like described above. Even then, it gets really hard to accurately measure fan airflow based on pressure differential. However, the RPM of a fixed pitch propeller is a pretty reliable indication of the thrust output, assuming no serious airfoil degradation like that resulting from icing.
How these two relate, I suspect, depends a great deal on the bypass ratio and the number of spools. I also suspect that limiting EPR is an indirect way of insuring that other parameters such as EGT and ITT are appropriately limited. This may explain why some manufacturers default to N1 when EPR fails; it gives accurate thrust, but provides no protection of core limits. On the other hand, some designs may simply be operating at such a derated output that fan speed is sufficient as a primary indication.
In the end, when operating a high bypass engine, you can have all the EPR in the world, but without fan speed you will likely be somewhat dissatisfied with the performance.
