The only other thing I can see that's different is this one the overload is on the delta contactor where the star contactor connects to where as it was on the main before.
This is important. If the overload was originally connected in the supply lines it needed to be set to the 38A FLC, not the 0.58x FLC (22A) which is the maximum permissible winding current. In delta it would have offered full protection, because tripping at 38A line corresponds to 22A winding current. But in star the protection was not adequate, because then the winding current and line current are equal and the 22A windings were running on a 38A O/L setting. This would mean that it did not trip so readily at startup and did not offer protection against serious overcurrent when the starter got stuck in star and the machine came under load, hence the fuses blew (what rating were they?)
If the new O/L relay is in the motor winding circuit, it needs to be set at 0.58x FLC and will protect equally well in both star and delta because it senses the winding current directly and always trips at the 22A maximum. Hence the new starter is more troublesome with this long, heavy start.
Steadily creeps down then the 30 seconds kicked in, got gowning on delta and was drawing 18amps.
18 amps line current even allowing for the magnetising current of a larger motor suggests it's taking 7-10hp of mechanical load at that time, just to rotate, without sawing anything. Mainly turning to heat; some of it is windage but much of it is oil in bearings and gears (assuming that motor also drives the feed?)
I don't do woodworking machinery but that seems a hefty load for a saw running light, imagine a dozen bearings each dissipating 500W, it would be glowing after half an hour. If the machine was cold for this test, perhaps the lubrication is too viscous. They can roll the blade around slowly for inspection but the bearings drag badly at speed until it warms up.
How closely equal are the line currents? I think if there is much of a discrepancy or the motor runs hot there is still a possibility of some shorted turns that are not evident on the coil resistance test. (You mentioned 60 ohms but can't be right otherwise it could never take more than 6.7A.) Is it possible to drop the coupling or belts and see how the motor behaves by itself?
The saw has two quite big cast fly wheels the band saw blade goes round maybe 3 or 4 ft in diameter
If by flywheels we are talking about the band wheels, although they are large and heavy the relatively low rotational speed means they don't store a huge amount of energy (which is proportional to the square of the speed.) I work on organ blowers that have shrouded impellers up to about 2'6" in diameter spinning at 1450 RPM which store enough energy to run on for a minute or two after hitting the stop. Plus the delivery has no backpressure at runup due to the reservoirs, so the whole thing is in overload until up to speed, and the longest I ever have to set the star time to is about 8-10 seconds. And yes, normal overloads sometimes complain on the larger units. Some have oil dashpots, some original 1930s starters don't have any O/L relay at all (!)
I doubt there is a coil phasing error even with the high current running light. The largest motor I have seen wired wrongly was a 5hp, which started in star and then had a crossed coil in delta, and that got so hot so quickly it set the smoke alarms off about 1 minute after startup and tripped a D32 MCB (1930s starter had no overload relay) suggesting the current was around 8-10x FLC.
