Some discussion (and links) about long-LOC endmills here.
Unless you really have to, I would stay away from super long LOC 1/8" endmills. On top of being hard to come by, they are bound to be fragile, at these lengths you would need to control deflection very accurately, which for a profile cut means you would probably need to reduce depth per pass to a very small value, and it will take forever.
If you can do a rough profile cut with a long 1/4" endmill, and then come back at the inner corners that require a smaller diameter, with such long 1.8" endmills, but removing much less material, you are likely to break fewer tools.