I haven't been able to reproduce the Mapbox mbtiles layer not loading without "network" connection - #4 by seewhy so I don't know whether the identified bug has been fixed.
Regarding pixelation / zoom levels, in my experience, PNG format tends to give better results than JPG if you zoom beyond the stored zoom level, but I haven't tried adjusting tile dpi beyond 150, mainly to keep file sizes manageable. What I have found is that in some situations and on some devices when I try to zoom past the highest level of my mbtiles layer it disappears and the underlying vector data shows - I haven't found a reliable way of reproducing that problem, so haven't reported it.
The issue you will find with vector maps is that you can't style different layers (unless that has recently changed) so if you have a complex drawing, it may not help you and the line thickness might be greater than the difference from pixelated raster.
I'm not going to teach you to suck eggs on accuracy, but honestly I can't envisage needing a basemap so accurate in the field that I couldn't use my eyes to locate myself relative to a point on a map / drawing - but then if you are doing as-built QA work or setting out a construction site, ODK might not be the best mapping tool
I can see what you're trying to do in terms of accuracy, and I'm not questioning that, but I'm not sure how widely applicable it would be to chase the highest zoom levels. I have experimented with basemaps of different types (usually taken from UK Ordnance Survey, but also 25cm resolution aerial imagery) and in the field I can't say the top end of zoom is much more help to me - and file size becomes a limiting factor for me.
Just to give some context, which might be of more general use than your specific case, I stop at zoom level 17 (~0.3m / pixel for my latitude) when generating basemaps for fieldwork - my built-in GPS only gives accuracy to 3m at best (with all the caveats of % certainty). This allows me, for example, to work on grids for data collection where points are 100m apart and I find I can navigate within 5m of a required point using placement-maps option for my geopoint. I would then probably use a photo if I needed higher degree of accuracy to relocate the point / quadrat. This works well with teams of enumerators.
I have recently started using a high accuracy gps for small projects and comfortably work to 0.5m accuracy (without RTK), and I could envisage using zoom level 18 (0.15m / pixel) if I was fully zoomed in.
I have been doing some drone mapping recently (and using ODK with the high accuracy GPS to map my Ground Control Points). After processing the data flying at 100m my map has a resolution of between 2 and 5 cm, so around zoom level 21, and absolute accuracy of (allegedly) 0.5m. But then in the field, I could use that only as a check that I'm within half a metre of where I think I need to be anyway, I suppose I could envisage trying to locate points within 10cm so at Zoom 22 that would be 10 pixels? But I'm potentially compounding my errors.
I am a strong advocate of sense checking my data - having a figure to 3 decimal places does not necessary mean it is accurate if the margins of error are above that - it becomes a false friend - especially if I am depending on data collected by someone else. My fear would be that using an ODK geopoint widget to check a location with centimetre accuracy could well be beyond its design limit and give enumerators an unhealthy sense of satisfaction and data managers a headache. It doesn't stop you recording the data at the high (e.g. RTK) accuracy now that @seadowg and others have developed that capability (thanks folks!). It might just be necessary to verify that data afterwards rather than in the field?
One thought though, having a scale bar on screen might be useful though to confirm how far beyond the maximum zoom of the tiles you've gone...
Sorry, long response, without a clear solution!