Sequence of total languages whose limit is turing complete
I'm not sure I full get your encoding and based on the comments there seem to be some problems with it, but I'll nevertheless provide my answer (or "answer", if you prefer).

A sequence of languages (your terminology) that satisfies your constraints is a sequence where the $i$th element in the sequence runs the Universal Turing machine for $i$ steps or until the machine halts, whichever comes first.

Clearly, each element in this sequence is total, but the limit is a Universal Turing Machine.