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.
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?