It doesn't sound like the OP understands the difference in a grounding electrode system and grounding/bonding of equipment.
The true "safety" he is seeking occurs through the bond between the EGC (equipment grounding conductor) and the grounded (neutral ) conductor.
The bond is to assure a low resistance path for fault current back to the panel (or source) so that the OCPD (breaker or fuse) can open the circuit due to the fault.
The GEC (grounding electrode system) has nothing (very very little) to do with the operation of the electrical system, especially it's ability to clear a fault. It is to, hopefully, divert lightning to ground and high surges that would result from high voltage faults such as the high voltage lines contacting the low voltage lines.
To the OP:
Do as has been stated. If you intend to stay with the 3 wire then bond the neutral and EGC and the panel cabinet (can) together. Also connect your conductor from your uffer to the neutral bar. Do not leave the neutral isolated. The way you have it now, if there was a fault between the hot conductors and anything metal from the equipment to the panel, it would not trip the breaker. In fact it would cause a voltage potential (shock hazard) between anything grounded and any metal in the path. All the uffer, rods, plates, etc you could put in wouldn't help in that situation.