I must be missing part of the question.
If you're interlocking two eyes and if it's three strand, you can't untie or undo anything, so why not make a good short splice as the securist way to join two lines, assuming equal size. No need in an anchor rode for the much harder to do long splice.
If you want to be able to take the lengths apart, then you need some sort of shackle connection. An eye over a thimble prevents chafe inside the eye but may subject the outside of the rode to more abrasion on the bottom. The same happens at the chain to fiber rode connection. For both, I like the crown knot (or sometimes two strand version) chain splice. It's like a marriage of a long splice and a back splice and Brion's books illustrate it.
In your application, do it on a shackle on each line and then just join by interlocking shackles.
I don't have good thoughts on what to do if you're looking at braided line.
G'luck
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