"A properly balanced sword is the most versatile weapon for close quarters ever devised… Its worst shortcoming is that it takes great skill, and patient, loving practice to gain that skill" -Heinlein
"Its practitioners are typically out of shape, chronically online, and have little experience with other martial arts"
True, unfortunately. Probably worth noting that this is not true of many of the top rated guys (eg. Kristian Guivarra and Sergei Kultaev, 4 and 5 here, are both (former?) boxers: https://hemaratings.com/periods/details/?ratingsetid=1 )
"HEMAs... core conceptual issue: that reconstructing a martial art from a few writings is incredibly difficult, and relies heavily on guesswork"
There's more than 'a few' writings and those from the Renaissance onwards don't require much guesswork, frankly. Joachim Meyer's 1570 text (on German fencing -- two-handed sword, sabre, early rapier, some other non-sword stuff), for example, includes pictures illustrating body mechanics quite explicitly, descriptions of techniques, and plenty of advice on strategy. Salvator Fabris (writing in 1606 on rapier) has all that and a far more accessible style to modern readers (Meyer is about as clear as that Musashi quote about stopping their cuts at c, ie. it makes sense once you've practiced swordsmanship enough). You're correct in that Medieval texts are pretty much just catalogues of techniques, often poorly described, and require a fair bit of interpretation but this is not universally true.
"competitions are few and far between"
"typically with restrictive and confusing rulesets that limit creativity and the use of physical strength"
I am a new HEMA guy and have only attended three comps so far (all in the past six months, since I started in 2020; few and far between indeed) but there have been no target or technique restrictions beyond don't strike the back of their head (which is poorly protected by typical fencing masks), don't punch, don't kick, don't grab the head or body (you were allowed to push or pull their hands in all three of them). This seems fair since it's supposed to be a swordfighting competition. The most arcane rules have been based on how long you're allowed to keep fighting once a blow has been struck but I'm not sure how that relates to creativity or physical strength (taking a sword to the face in order to get a hit is bad strategy). In the interest of not being disingenuous, one comp I attended had narrow rectangular 'rings' that made nonlinear movement impossible but that's not typical -- and there was a lot of complaining about it. Perhaps you would like to provide some examples?