I like the idea of connecting pin 13 to +5V to skip the bootloader. You might need to disconnect it to upload code, but that's better than needing to disconnect RX just to reset the board. Especially because pin 13 is probably only rarely used as an input (although it is one of the SPI pins, which might mean that it gets tied high sometimes).
As for burning the bootloader, you might try the USBtinyISP from adafruit industries: USBtinyISP AVR Programmer Kit (USB SpokePOV Dongle) [v2.0] : ID 46 : $22.00 : Adafruit Industries, Unique & fun DIY electronics and kits. It's not yet supported from the Arduino environment, but I just got one and hope to add support at some point. For now, it should work from the command line with their custom version of avrdude, but I haven't tried it yet.