Gap between bottom of shower wall and tub is too wide to caulk (~1"). What to use?

[stuyguy]

When I tackled this job years ago I ended up using what seemed like gallons of silicone caulk to fill the very wide space (about 1') between the bottom edge of my shower wall and the top rim of my bathtub. The job did not come off well -- eventually the caulk shrunk and separated from the bottom edge of the wall (but it stayed firmly attached to the tub), and the whole thing mildewed in the nooks and crannies. I'm sick of it and want to start over.

I want to use something like a strip of molding that would seal the gap. Ideally, it would attach to the bottom of the tile wall and "hang over" (and cover up) the existing caulk, allowing water to drain past the open shrinkage crack.

Now, I know they make tile pieces for tub edges that are about 6" long with a hollowed quarter-round cross-section, but I don't want to use those things. First, I don't want to get into any serious tilework here. Second, the shower wall is made of natural marble tiles and those quarter-rounds are generally made of glazed ceramic; I'm not crazy about the mismatch. Third, there is not much of a shoulder on the far edge of the tub, so the quarter-rounds would end up looking real sloppy back there, especially if a rookie like me is installing them.

I'm open to other suggestions and tips, however.

Thanks all, in advance!