2. Are you sure your configuration option "attiny13.name=Attiny13 @ 128 KHz (internal watchdog oscillator)" works as expected? In my case IDE says it is missing "upload.tool=arduino:avrdude" and ".bootloader.tool=arduino:avrdude". However, having added those I must have locked my ATtiny13, it does not respond anymore.
P.S. May I take some more time to read the whole thread? :) I definitely must not be the only one to try this 128KHz option :)
I've used the 128KHz many times. The issue here is the tiny13 cpu clock is too slow for some ISP programmers SCK clock speeds.
In order to program at these very low speeds is you need an ISP programmer that will support the Bitclock rate adjustment from avrdude -B option. There are several programmers that will support this option, AVRispMKII, USBtinyISP(some versions may not work correctly), and USBASP(new firmware versions). I've even add my own 16KHz clock rate option that works with this bitclock rate adjustment.
ArduinoasISP will not work at these very slow speeds.
For avrdude -B option, you should specify at least -B50.
To program via the IDE, then you will need to change the Global defaults in the avrdude.conf file.
Some where around line 335:
# Overall avrdude defaults; suitable for ~/.avrduderc
default_parallel = "lpt1";
default_serial = "com1";
# default_bitclock = 2.5;
default_bitclock = 50;