I wouldn't say that there is an elliptical I would do in the sense in which elliptical is normally used.
Generally, elliptical constructions are more explicit:
I ate chicken and then [I ate] dessert.
Here, I ate is already used in the first part of the sentence, so it's omitted presence is easily assumed in the second part of the sentence.
Or:
Did you have chicken for dinner?
Yes [, I had chicken for dinner].
Answering yes or no is commonplace, and the omitted information from the question is easily assumed.
That might have been a far-fetched argument. But anything to make my point.
You might look at your construction as an example of an elliptical sentence. But I think it would be putting too much of a burden on the reader. There is no obvious context from which I would do can be taken as the missing phrase.
You have struggle briefly to come up with omitted words that make the second sentence complete. In fact, first I try to change the punctuation. Then I consider what else would make it work. It took me about ten seconds to come up with I would do as a possibility.
Any construction that causes a reader to pause or backtrack in order to parse it should probably be rephrased.
In this case, it seems fairly trivial to add that missing I would do—so, why wouldn't you?