I scavenged an AA boost driver from a cheap zoomie and it uses a ME2180 DC-DC regulated output voltage chip that might be of interest.
A picture of the driver can be found in my build post.
The datasheet can be found here.
Here is the website for the company that makes this chip.
http://microne.com.cn
Many of their step-up DC-DC converters look suitable for an LED driver because they only need two external parts: an inductor and a capacitor. Since these are voltage regulators and not current regulators like the PAM2803, they are better suited to power the ATtiny.