As I said I would, I replaced the bias resistor R15 (1k8) for T4 with a potentiometer, which just happened to be on the bench and a value of 4k7. Monitoring the base voltage with one eye, and the current drawn with the other, I adjusted the value of this pot. At some high value, the current actually dropped!, but as the resistance was lowered, I hit the point where the transistor would go into thermal runaway, the current climbing, slowly at first then exponentially faster, up to several hundred mA!
Several attempts later, and I hit on a setting where the meter needle stayed put even after watching for longer than it took to start climbing before. Measuring the pot (and the original resistor, they were in series) gave a value of 2800 ohms.
I replaced the pot and original R15 with a 2k7 unit, but this was too low and the current started to climb. A value higher, 3k3, and the current stays where it is on the meter needle, a total circuit current of around 75mA. I had already measured the circuit up to but not including the driver at 60mA, so the Tx driver is now set taking about 15mA. This might still be too high, but at least now seems stable! Ive asked for confirmation and advice on the G-QRP club forum, that ive done the right thing here.