Look to the vacuum setup to the power brake booster. The booster itself can have an internal leak or the plumbing from the carb to it may have developed a leak.
The tube itself is steel and can develop a pinhole from rust where you can't see it or the booster diaphragm itself can be leaking.
As far as the timing causing this, it can be but if the timing light is showing correctly be aware that with the 4v balancers it is VERY COMMON for the balancing ring to have slipped. That can account for the actual timing being retarded while the balancer actually showing that it is ok.
It only needs to be off a few degrees to do this. A 351c set at 0 to 2° can cause this.
The only way you can find this without pulling off the balancer and having that ring position checked is to set the timing up, i.e., advance it and see if the dieseling stops. With an original untouched balancer you have a high likeliness that it has slipped.
You can have them rebuild so no need to panic but it will just be "down" while it is out for a rebuild.
For your information, the 4v balancer that was supplied new on the 351cj engines is not the best balancer to use. The D1ZZ Boss or the D2ZZ HO balancers would be.
The difference between the two would be the factory balance on them. The D1 is matched to the factory domed pistons while the D2 is for the dished pistons. You can run either together since the difference in balance is not something you normally will see until high rpm's.
The D1's are expensive and rare but the D2's occasionally come up used for sale. There are more 351 HO's out there then you would expect.