Whether は can be inserted in [V1]-て[V2] seems to be determined less by the combination of verbs itself than by the function of the て-form, which, of course, restricts combinations of verbs.
It works best when [V1]-て[V2] makes up a compound verb to express one idea.
追いかけてくる in your examples all satisfy this condition as you observed.
Other examples include:
It also seem to work if the て-form of V1 expresses either a means or attendant circumstances, but mostly in a negative sentence that emphasizes that the action of V2 is not performed by the said means or under the said circumstances.
I’m not very sure if this は should be considered part of the [V1]-ては[V2] construction you asked about.
I cannot think of an example that sounds natural, not even a negative one, in which the て-form of V1 expresses a cause, a reason, or one of a series of actions.
座って落ち着く in the other answer,
座って can be interpreted as expressing either a means, attendant circumstances. or the first of two sequential actions. Either way,
座っては落ち着く doesn’t make much sense. If I had to make some sense out of negative
座っては落ち着かない, I would understand it as meaning this person chooses to relax not by sitting but by other means.
飲んで食べる, which I used as a counter example in my comments above, also describes two actions except they don’t necessarily happen sequentially.
飲んでは食べる is possible but it describes a way someone repeats to drink and eat alternately and doesn't have the emphasizing effect.