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Yes, you could install an E4OD. It's a four speed overdrive transmission. Make sure to get one that was attached to a 460. There are different cases, and they do not interchange.
You will need to move the trans crossmember back, because this trans is longer than the C6. You'll also have to shorten the driveshaft. But these are the easy parts.
The harder part is you need something to generate a vehicle speed signal. You'll need to invent something. Then you need a wiring harness and a computer system to run the trans. There are aftermarket computer systems that may be a bit easier to make work than a factory system.
Maybe you just need the C-6 sreviced or worse case rebuilt or even some modulator changes made? Do you have the correct modulator in it? Does it maybe have a PO installed shift kit? Are you sure it is working 100% right. What are the symptoms? High reving (more than normal), then a hard up shift? Or a hard down shift? I bet Mark could help trouble shoot it, before you go all E4OD down the rabbit hole.