PE6 is tough I think, as for me I find most Carpenter PE6-8 GT rods lean more towards PE8. For example, Super Popping 80M is for me more of a PE8 rod. That's all fair enough as I guess PE6 is not used that often for GT fishing.
For the lures you mention, DJ83MH would be a good call but not with PE6.
EP82/38 will be great with the lures but is more of a PE8 rod I think.
EP85/36 might be the one.
Also James, I would suggest you do not necessarily assume that a longer rod will cast further. Sometimes that is not the case and a lot depends on the nature of the blank and how you cast. For example, I think I can cast Coral Viper 79/40 as far as I can SP80M.