I've truthfully never looked at the charging circuit to any degree. It's interesting that it starts with 2 volts, that sounds like they're trying to protect against a shorted battery. If so, that would also help with the supercap as it looks like a short at first until it gets a charge. However, going from 2 volts charge to the full 9V charge would still put around 7 volts across a very low impedance load, that being the supercap. That still gives me 2 watts across that half-watt resistor.
I have a similar charging issue in my YLB - RailSounds Battery Replacement, I start out with a totally discharged 1.5F supercap and apply 5V through a 10 ohm resistor. That gives me 2.5 watts at the resistor until I get a voltage of at least 1 volt on the cap and it down to 2 watts. I can tell you that the 10 ohm resistor gets pretty toasty in those few seconds as the cap charges, and I'm only at a max of 125% of the rated power of the resistor. Dumping 400% of the rated power into a 1/2W resistor, even for a short time, isn't going to be particularly good for it.
