Perhaps I should risk soliloquising, and add further to that.
Stephen Hughes wrote:a large outer garment, with an cross over design tied with a single waist cord,
The reference to a cross over design might be a wrong speculation here. The verb (or verbs) ἐνδύω / ἐνδύνω etymologically (at least) refer to what is put on over the head, rather than wrapped around.
Besides that, here is some of my other thinking about it ... If τὸν ἐπενδύτην διεζώσατο is composed of two parts, "the outer garnent" and "put on his belt", like our English "he is tying up his shoes", it would imply that the ἐπενδύτης was hanging loose about his body (or that the shoes were on his feet), and that he then tied the waist band/belt to steady it in place before swimming, but that is incongruous with the following statement ἦν γὰρ γυμνός·, because to be "scantily clothed" does't mix with having the outer garment on (cf. 2 Corintians 5:3 εἴγε καὶ ἐνδυσάμενοι οὐ γυμνοὶ εὑρεθησόμεθα. (Byz. phrasing)). This phrase in John 21:7 is clearly a narration of some events, so it may not be able to take the clothes and belt in such a separated manner as they are presented in the descriptive text of Mark 1:6 Ἦν δὲ ὁ Ἰωάννης ἐνδεδυμένος τρίχας καμήλου, καὶ ζώνην δερματίνην περὶ τὴν ὀσφὺν αὐτοῦ, καὶ ἐσθίων ἀκρίδας καὶ μέλι ἄγριον. As a speculation about what was not written here, as a comparison to what is written, some other obvious verbal phrases to consider here might be the (speculative) cognate accusative phrase τὸν ἐπενδύτην ἐνδύσασθαι "to put on one's outer garment", or just simply the (attested - 2 Corinthians 5:2) verbal phrase τι ἐπενδύεσθαι "to put sth. on as one's outer garment".
But, if τὸν ἐπενδύτην διεζώσατο, were a whole phrase implying the entire process, expressed by just mentioning the last step, like our English, "once you put the finishing touches on the cake, we'll light the candles and sing Happy Birthday.", with the sliced fruit and the belt being the final steps in the cake making and dressing processes respectively, then the sense of the whole phrase τὸν ἐπενδύτην διεζώσατο might be expressed by, "once he had finished getting his outer garment on", with the belt being considered part of the attaire. That is seen in the two other similar uses of ζώννυμι "I'm putting my belt on" in the sense that the final action represents the entire process, "I have gotten dressed ready to go out" in the same chapter as the phrase we are duscussing comes from: John 21:18: Ἀμὴν ἀμὴν λέγω σοι , ὅτε ἦς νεώτερος , ἐζώννυες
σεαυτόν, καὶ περιεπάτεις ὅπου ἤθελες· ὅταν δὲ γηράσῃς, ἐκτενεῖς τὰς χεῖράς σου, καὶ ἄλλος σε ζώσει
, καὶ οἴσει ὅπου οὐ θέλεις. The entry in BDAG seems totally logical and sound in the light of that. The example of διαζώννυσθαι ἐσθῆτα, in LSJ is also an obvious parallel. Moreover, the usage of περιζώννυμι, in Luke-Acts and Ephesians for "I am getting dressed" is also similar. The example of διαζώννυσθαι ἐσθῆτα, in LSJ is also an obvious parallel of διαζώννυσθαι of "get oneself dressed" using this final-action-in-the-process (putting on the belt) summary method of constructing meaning, and a cognate accusative of what somebody has been dressed in. In Revelation 1:13, καὶ περιεζωσμένον πρὸς τοῖς μαστοῖς ζώνην χρυσῆν, however, the belt - the thing wrapped around the waist - is also describe (cf. Revelations 15:6 also a descriptive rather than a narration of the flow of events) uses the middle voice of a ζώννυμι verb.
Luke uses δῆσαι of Agabus at Acts 21:11 καὶ ἄρας τὴν ζώνην τοῦ Παύλου, δήσας τε αὐτοῦ τοὺς πόδας καὶ τὰς χεῖρας presumably
because the appropriate verb to use is the one dependent on the place that things are "tied" (in the case of hands and feet, the δεῖν is translated "bind", but the meaning is implication, "constrain the movement of"), rather than the verb usually used with the object - ζώννυμι with ζώνην - goes with that object to the new location. (As an aside, LSJ's example in the διαζώννυμι entry of διαζώννυσθαι ἀκινάκην "to have a short, straight sword bound into one's belt", might suggest that if Luke had written διαζώσας τε αὐτοῦ τοὺς πόδας καὶ τὰς χεῖρας Paul wouldn't have had a problem with the hands part, but would need to be a contortionist to get his feet into the belt too. Back to the point...). Building on that presumption
, we could look at the last part of the LSJ entry, which in the metaphorical section (a bit disorganised in tbe 1940 edition) of the διαζώννυμι entry talks about things that are worn around around other things like a girdle. In the metophorical part of the section before the metaphorical section, ἀρχὴν is the accusative with a middle in the phrase ἀρχὴν διεζωσμένος "invested with an office", or literally, "wearing an office as a girdle". The double reference of the accusative in John 13:4 λέντιον διέζωσεν ἑαυτόν, may be another example of this "wearing as a girdle" meaning.
If Peter was getting dressed expecting to walk, we wouldn't read the very strong statement ἔβαλεν ἑαυτὸν εἰς τὴν θάλασσαν but rather than Matthew 14:29 Καὶ καταβὰς ἀπὸ τοῦ πλοίου ὁ Πέτρος περιεπάτησεν ἐπὶ τὰ ὕδατα, ἐλθεῖν πρὸς τὸν Ἰησοῦν. that would be similar to getting out of a vessel high above dry land.
If in this phrase in John 21:7 τὸν ἐπενδύτην διεζώσατο, it could also be taken as a non-metaphorical example of the meaning "wearing something as a girdle", that would make much better sense for somebody who was trying to swim to shore. There are good and logical reasons why τὸν ἐπενδύτην διεζώσατο can be taken as desribed in BDAG, and I have set possible reasons why that entry makes sense. For the wearing of the towel, as a girdle that is sort of logical, because people do that after having their showers or going swimming. If Peter was getting dressed on dry land, the meaning given in BDAG, is I think great. If it was for somebody about to swim, however, tying the clothes around the waist like a girdle seems safer.