"Do" as a tense marker

Solution 1:

Yes, though I wouldn't call it a tense marker.

As well as its use in questions and negations. do may be used in declarative sentences in Modern English, in certain circumstances:

• In contrast to a negative question or suggestion:

I know you don't like swimming. Yes, I do like swimming!

• For emphasis or positive affect (often with an intensifier such as certainly or really:

I really do intend to get some work done today.

I do like ice cream.

He does look like his father, doesn't he!

You're right that Shakespeare used positive do apparently without any special meaning.

[Not an answer, but I think you're complicating matters by talking about moving the -es and the -d onto the main verb. If you find that a helpful mnemonic, fine, but it's not really what's happening.]

Solution 2:

As I recall, Chomsky's 1957 analysis had an abstract part of the auxiliary system called EMPH (for emphasis) which required application of the Do-support rule even when there is no negation or inversion: "Henry DOES like fish." The apparently pointless abstraction always bothered me. Why not instead just suppose there are are auxiliaries "do"/"did" which express tense, and if they are stressed, remain, otherwise cause the following verbal element to be suffixed ("Affix-Hopping" of /-d/ or /-z/) and drop out?

So, if that's the idea behind the analysis you're talking about, yes, I like it. But I doubt it corresponds to what happened historically in English.