A couple more points here, you've got a lot of volume in most boilers! It's going to take time for a hot fire to make the water hot.
My suggestion would be to do a few things with steamers in this situation. First would be to place the loco in a 'shed' road... Then, go back to the loco about 5-10 minutes before you need it and put some coal in (and water if it's below about 60-70%), and crack the blower a little (press N once IMO). At the same time, move the loco from the shed road, to a 'train ready' point (e.g. if there's a turntable, move to the turntable, turn if necessary, then out to, say, a water column to top up the tender). This will drop the boiler pressure, but you should now get a realistic indication of how the loco is going. If needed, open the blower a little more (depends on how low the pressure is). Now finish your shunting (put it down to the shunter having to wait for another train

- You could always have an AI train setup to 'cause' the stop in shunting

), and then when you're ready, go back to the larger loco.
Note, it's generally good practice to be 'close' to full pressure, but not too hot, when you bring a loco onto the train. Then, whilst you do the brake test and wait for departure, you make it truly hot. You'll generally have a good 5-15min at a minimum wait at a station, at least that's what I've seen in Aus, plenty of time to go from '90%' to '99%' pressure. When you're making pressure, you know you've got a reasonably hot fire.
If you're using TS12 SP1, and you're running a passenger service, I'd recommend putting the rule 'Advanced Industry Load Configuration' and setting up at least the first station. Untick the option for 'Lock Train Controls during Loading', that way you can keep warming it up (and putting in water if needed) right up till departure, whilst still loading passengers. You might also want to put it in for other stations as well

That way you can prevent blowing off as much as possible!
Zec