Currently I’m looking a bit into older research on Mansi. Coverage on the language has not been optimal in the past, mainly due to most of the existing field research materials being rather slow to be released. The main sources on no less than a 100+year-delay! — Bernát Munkácsi’s 1880s records coming out in dictionary form in 1986, Artturi Kannisto’s 1900s records in 2014, and Antal Reguly’s 1840s records I’ve not seen any decent edition of at all. I think this has left etymological research in particular in a limbo. Mansi specialists with direct access to one or more of these field research corpora (e.g. Steinitz, Liimola, Kálmán, Honti, and of course Munkácsi and Kannisto themselves) have for long been able to dig out comparisons and publish their findings, but us more general Uralicists not so much.
Many of these Mansi specialists have also been working with Khanty, whose primary comparative lexical source, K. F. Karjalainen’s dialect dictionary likewise built on 1900s field research, came out already in 1948, making the language more accessible for investigation. This has, I believe, led to a kind of an “overlooked middle sibling” status for Mansi, creating a more Khanty-colored picture of the language’s history than is warranted. Comparisons between the two languages are much more readily apparent than more distant cognates. Yet it can be also suspected that many of these are not common Ob-Ugric inheritance, but rather newer loans (Ms → Kh, Kh → Ms, or from some common third source). We also know of a cautionary example from the western end of the Uralic family: untangling Finnic loans from true cognates, with the help of more distant relatives, has been integral to working out the history of Sami. This line of work has by now revealed that just about all especial commonalities between Finnic and Samic are either archaisms, loans, or areal, and that from a proper cladistic point of view, a Finno-Samic subgroup is really no stronger supported than some different hypotheses such as Finno-Mordvinic would be.
For Mansi and Khanty, this work has so far not been done … but I strongly suspect the results would have a similar lean. Extensive areal sharing of some secondary isoglosses is already well-documented along the Mansi–Khanty contact zone. There are also a number of known Mansi–Hungarian and even Khanty-Hungarian isoglosses, as well as several “Proto-Ob-Ugric innovations” that appear essentially out of the blue.
These considerations suggest some steps for going forward. One that could be done without too much trouble with just the existing materials would be to “re-root” the historical phonology of Mansi in Proto-Uralic. E.g. as has been established at least since Sammallahti (1988) (more debatably already since Steinitz 1944), the regular reflex of Proto-Uralic *ä in Mansi is *ää — a development that surely represents simple qualitative retention, and not a detour through a Proto-Ob-Ugric *ee (as per Honti) or *eä (as per Sammallahti). Corresponding mid *ee in Khanty is most likely an independent innovation (likely even post-Proto-Khanty, as per the reanalysis due to Tálos of Surgut Khanty /ä̆/ as more original than other varieties’ /e/).
But etymology will require work too. A Mansi analogue of Steinitz’ comparative-etymological dictionary of Khanty would be quite desirable, now that the main sources are finally out and available for easy consultation. This would doubtlessly take an additional long while to assemble though. Also, from the comparative Uralist’s view, this would involve lot of work being spent on clearly secondary material: compounds, derivatives, relatively recent Russian and Tatar loans, etc.
I have at this point a shortcut of sorts in mind. The Munkácsi and Kannisto materials have been the main sources for comparative research on Mansi for the last 140 years, and we might assume they have been already reasonably mined through for comparative purposes. They’re far from the only materials on Mansi though. Older collections could be still expected to maybe have some archaisms in them that have been lost in later times. We again know from precedent that this line of research is likely to bear some fruit. On historical phonology, the 1970s-80s “Hungarian school” (L. Honti, K. Rédei, E. Sal) revamp of Proto-Mansi reconstruction has been based on 18th-century records that show some retained word-final vowels, pointing to stem-type contrasts CVCə | CVC and CVCCə | CVCəC (from the 19th century on, collapsed to just CVC and CVCəC). This then can be leveraged for some reanalysis. — On etymology, there is so far at least a small 1991 article by Katz: “Altsüdwogulisches” (FUF 50),  which identifies from 18th-century records previously unknown Mansi reflexes for PU *kota ‘hut, house’ and Indo-Iranian → Ugric *täjɜ ‘milk’.
The 18th century materials are, alas, still not well-documented in print. The Hungarians mainly refer to a manuscript Altwogulische Dialekte by J. Gulya, which I believe ended up never being published (though some of the data is briefly covered in his articles in NyK 60 and 62). So I’m casting my hopes into the 19th century instead. There is too at least one smaller primary source to have been released relatively timely: A. Ahlqvist’s materials starting since the late 1850s, a wordlist of which was released in 1891, as the second SUST volume Wogulisches Wörterverzeichnis (and by now available digitally; also on archive.org, IMO in better scan quality than the National Library of Finland version). The usability of this data is limited somewhat by various dialect forms being given without specifics — perhaps Ahlqvist’s original records would have this info? — but with modern Mansi dialectology in hand, the big picture is clear enough. I am not aware of any later reappraisal of this material, and it seems likely that a close look could turn up some new etymological insights.
As a promising initial result, from the A section I have already run into an entry aidentantqtam ‘to vomit’. As Ahlqvist seems to render unstressed schwas varyingly as a, e, i, i̮,  as well as coda /ɣ/ often as a vowel i or i̮, we can thus see this as a reflex of PU *oksənta- ‘to vomit’ > PMs *aaɣtəntə- (showing several regular developments: *o-ə > *aa, *s > *t, *kC > *ɣC).
In overall phonology it is also interesting to note how, while most of Ahlqvist’s data seems to be Western Mansi, he has also numerous forms showing the Northern Mansi development *ä > /a/ (e.g. mań ~ mäń ‘daughter-in-law’, ńäl ~ ńal ‘handle’; notice also the inconsistent lemmatization), sometimes quite tellingly further combined with also typically Northern *š > /s/ (sam ~ šäm ~ šem ‘eye’). Yet, his examples of the combination *kʷä- show uniformly only küä-. In newer Northern Mansi this has undergone a shift to /o/, starting from Munkácsi’s materials, but no sign of this appears in Ahlqvist’s materials. Perhaps this is then indeed independent from the usual NMs shifts *ä > /a/ and *a > /o/ (it could be otherwise routed through either), and has instead proceeded as something like /kʷä/ > *[kʷɞ] > /kʷo/ > /ko/?
— Edit 2019-01-11: nope: one doublet jelpi̮l-küäl ~ jalpi̮l-kol ‘church’ (lit. ‘holy house’), already seems to show the native NMs reflex. There is also plain kol, though given separately, not coordinated into the same entry with the WMs form küäl.
 Why specifically “süd” is unclear to me, given that some of his forms are clearly Northern Mansi.
 Theoretically some of this variation could represent real vowel contrasts, neutralized in later times, but that will require a more systematic look at the data, maybe with dialect division included.