The biggest difference between microwave and hot plate digestion is throughput, safety, and convenience. If you do a lot of ICP-OES, it's worth the investment. Not sure why the HF is necessary, usually it's only needed for silicates. Avoid at all costs if you can, that stuff is nasty. White lead is mostly carbonate and hydroxide. I would think strong acid would be sufficient unless it's a really impure mineral. If it's a geological sample that has a lot of other rock/sand/soil in it, this might be why the other method uses HF. If it's a pretty refined lead carbonate/hydroxide, it probably isn't necessary.
What instrument are you using? Our ICP-OES provides common spectral interferences for most elements. Probably yours will too.
I assume you are using high quality (trace metal at minimum, optima better) acids? Have you checked to see whether your tartaric acid has contaminants in it? We were doing a digestion once that used a weird acid in the matrix and it was found to be the source of a trace impurity that was giving us headaches. Any idea what the tartaric acid is for?
This is totally a stab in the dark, but has anyone tried an ashing method? Carbonates are prone to pyrolysis.