With your indulgence Jonathan, and not in recalcitrance, I'd like to say something about guessing before moving on to Mr. Milton's grammar.
Here is a simple example:
Question: What is the square root of fifty?
My thought process if I have to guess: Well, the square of seven is forty-nine and the square of eight is sixty-four, so it is greater than seven and less than eight. Also the interval from forty-nine to fifty is one and the interval from fifty to sixty-four is fourteen, so the interval between seven and the square root of fifty is less than one fifteenth of ten.
My guess: seven point zero six.
(The correct answer is 7.071067)
There are a number of mathematical skills that I used to make my guess more sure or reasonable. Those are things that I am able to do myself because of previous knowledge, drills and experience. Assuming that there is an element of guesswork in composing Greek, how can the guessing be checked? We are not trained in Greek usage, when we are trained in seminary, because there was (for me at least) no compositional component.
In learning to compose, there is an element of guessing, and unfortunately, there are no neat and readily available models to check one's guess against. To turn now to do what Jonathan asked about sticking to the grammar, let me layout a few details about this construction, and how to use it in composition.
In Mr Milton's latest practice sentence - ἐν τῷ θεραπεύειν τὸν Ἰατρόν τὸν άνθρωπον, ἐγένετο σεισμός from "As the doctor was treating the man, there was an earthquake. " - there is generally no problem, so long as earthquakes can make up part of a doctor to patient treatment process. His Greek sentence means something like, "One of the things that happened as a sequential (temporal consideration), but not intentional or planned (volitional consideration) part of the doctor's treatment of the man was an earthquake." Leaving off both the temporal and volitional dimensions, and only stressing the overall (persistent) nature of the action, the ἐν τῷ + inf. here could be translated as, "A event that occurred that involved the doctor and (in this case also) the patient as part of (be reasonably expected to happen during the course of) the treatment (without putting an end to what was happening!!!) was an earthquake." The authority structure between doctor and patient suggests the doctor might be in control, but that control or power structure is limited to the phrase θεραπεύειν τὸν Ἰατρόν τὸν άνθρωπον, and doesn't extend beyond the the limits of the ἐν τῷ + inf. phrase. In other words, there is an independence of will between the action of the earthquake - which Mr. Milton correctly indentifies and uses, but there is a problem with the semantics of θεραπεύειν.
What makes Mr. Milton's translation implausible is not the Greek grammar or syntax, but the lack of relationship between θεραπεύειν and σεισμός. More specifically, if somebody wants to compose using this ἐν τῷ + inf. there are a number of constraints on what can be said. It is a tight-packed structure, unlike the more broad reaching "while" of English. That care or caution needs to be taken because the structure prompts the reader to think that there is a relationship between the two actions - in other words, it has to be reasonable to expect that what happens outside the ἐν τῷ + inf. could be part of that process or sequence, and there must be a separation of wills (avoid syntactic monotheletism) or accidents (if we are speaking of non-volitional entities). While volition is separate, flow is not.
In using this construction, there should be a movement from vague focus or large picture, to a specific incident or detail - usually expressed by a word whose meaning has limited scope, ie. one which is very specific.
My suggestion for Mr. Milton's improvement is that he learn vocabulary in a structured way, similar to "prepare food - slice, dice, stir-fry and serve", which we immediately recognise as only one possible sequence of cooking in English, but in a second language one needs to (at first at least) artificially construct such taxonomies.
Here is a quick discussion of some examples; Matthew 13:4 - ἐν τῷ σπείρειν αὐτόν, ἃ μὲν ἔπεσεν παρὰ τὴν ὁδόν - σπείρειν is scattering seeds describing the entire process, their falling where is incidental. Matthew 27:12 - ἐν τῷ κατηγορεῖσθαι αὐτὸν ὑπὸ τῶν ἀρχιερέων καὶ τῶν πρεσβυτέρων, οὐδὲν ἀπεκρίνατο. - κατηγορεῖσθαι is the whole kit and caboodle, not just saying "You did such and so." cf. Acts 24:2ff, while ἀποκρίνεσθαι is one small step in the process. They weren't looking for the opportunity to blurt out, "You're wrong!", they fully wanted to "drag his arse into court" (as the Americans say). Mark 2:15 - ἐν τῷ κατακεῖσθαι αὐτὸν ἐν τῇ οἰκίᾳ αὐτοῦ, καὶ πολλοὶ τελῶναι καὶ ἁμαρτωλοὶ συνανέκειντο τῷ Ἰησοῦ καὶ τοῖς μαθηταῖς αὐτοῦ· - do other people sometimes join one for a meal? Yes. Was their seating themselves their choice? Yes. Moreover, κατακεῖσθαι is a more general word than the prefixed συνανακεῖσθαι. Luke 2:6 - Ἐγένετο δὲ ἐν τῷ εἶναι αὐτοὺς ἐκεῖ, ἐπλήσθησαν αἱ ἡμέραι τοῦ τεκεῖν αὐτήν. - a broad and general situation followed by a specific event that could logically be expected to happen to a pregnant woman. Luke 3:21 - Ἐγένετο δὲ ἐν τῷ βαπτισθῆναι ἅπαντα τὸν λαόν, καὶ Ἰησοῦ βαπτισθέντος καὶ προσευχομένου - Jesus came as one of the many, which is both logical and a contrast between the large picture and the small. Acts 4:30 - ἐν τῷ τὴν χεῖρά σου ἐκτείνειν σε εἰς ἴασιν, καὶ σημεῖα καὶ τέρατα γίνεσθαι διὰ τοῦ ὀνόματος τοῦ ἁγίου παιδός σου Ἰησοῦ. - there is something of an (implied) causal relationship here, but it is not expressed syntactically (the second infinitive following the δὸς of verse 29. 1 Corinthians 11:21 - ἐν τῷ φαγεῖν, καὶ ὃς μὲν πεινᾷ, ὃς δὲ μεθύει. - the general situation and two distinct possibilities.
If Mr. Milton would like some specific exercises or drills to improve his use of this construction, and was unable to design them himself, then we could discuss that here too.
If you have gotten used to that construction already, we could say at a more theoretical level that the use of ἐν in this construction, is not the "space within which" ἐν that works with a homogeneous whole, but rather "one of the constituant parts" ἐν that works with something composed of a conglomeration of things into a whole. A prerequisite to understanding that, is that there is a need to differentiate between simple actions or entities and complex ones, as described in passing above.
Γελᾷ δ' ὁ μωρός, κἄν τι μὴ γέλοιον ᾖ
(Menander, Γνῶμαι μονόστιχοι 108)