Hello,
Thank you for your background, it helps frame my reply.
Nice to meet you 
This is my “take” on all this, with references you can follow up (I won’t mention the rabbit-hole you are probably already aware you are in!)
… trying to find an identity?
Historical - as you would already know, the recorder goes hundreds of years back to about 1400, and evolved in all the various countries with different translations of its names and sizes, with the different makers throughout the centuries. With illiteracy, limited communication and travel, (semaphore, morse, pigeon tags, phone, internet, airplanes yet to be invented) it is not surprising our problems with a universal “name” for each model of recorder.
Aside: recorder developments continue to evolve with modern makers studying originals from the various museum instruments or drawings available, copying, tweaking (for example Vincent Bernolin’s Historical reenactment program), the use of high definition scanning, 3D printing (resins, wood-based resins) to the development of the “modern alto” (yes, that’s its name, at least for now.)
A good example if you are interested, is the name “voice flute” with apparently a very convoluted historical background of its “name” as outlined by Sarah Jeffery.
Nomenclature
Helen Hooker has this chart
You might like to read the article it came from.
Her website for recorder information
“Sub-bass”
If I know it is an experienced or professional recorder player referring to the “sub-bass” I assume it is the Contrabass, but sometimes someone will say “sub-bass” using “sub” meaning there is a “sub” in its name … and “bass” meaning one of the bass recorder models—so sometimes I am not sure (maybe it is just me!) Perhaps adding “in F” or ”in C” helps because then you might be able to determine which is being referred to. As you see, there are a number of “sub” named models.
Clefs, transpositions
From another of Helen Hooker’s articles
“Bass recorders” are a group of the lower pitched ones (generally bigger in size), with the smallest of the bass sizes often called the “Basset” recorder as you found out, it having a cute name all of its own.
All bass recorders are generally (!) notated with bass clef (with various octave transposing)
Basset is notated in treble or bass clef, Sarah’s explanation but her definitive preference is the bass clef.
Transpose according to octave
Sarah: all models, written vs sounding pitch. This should answer your questions
I see Sarah’s summary sheet shows the Great bass as non-transposing (octave) (which leads to ledger lines) then buried in the discussion below, she admits it is incorrect.
Dorico
If you are only notating for yourself, then go ahead with treble clef. Listeners will only care about the aural, not how you cognitively got it to there. You are not alone as you already know for the reasons you outline.
Dorico alternative instruments
As you know, the definition of a single instrument has a setting for which clef in the score, another setting for the clef in the part, so you can create two (or more) alternatives of that instrument and assign them to whichever layout you want to create (see below.)
For the bass “recorder instruments” as you have already decided, have one with bass clefs (part and score), another with treble for the part instead.
Related threads from this forum
Instrument definitions for recorders
How to create custom instruments (recorder)
Dorico layouts
Dorico allows you to have different layouts (you might already know this) where you can choose different instrument selections for the same piece (meaning your different instrument alternatives, depending on clef preferences.) You might like to provide different alternatives for score and parts, so no player is embarrassed, they can select whichever they prefer and you won’t have some struggling at a rehearsal/performance because they are attempting to read from the “wrong” clef. Just copy/paste to the alternate instrument and set up your layouts.
For the score, clefs used might depend on the conductor it is destined for (a recorder player as conductor, might only know treble clef, so could prefer everything in treble, perhaps with the appropriate 8 or 15 … (22, 29, 36, haha!) designation below the clef.
Aside: Dorico has 8 and 15 in the instrument definition options, but there are others in Dorico’s Bravura font. Perhaps treble clef 22 below would work for alto players playing a sub-contra?
You will find information on Dorico layouts with any kind of search, our Dorico user manual, videos, or threads here.
Bass clarinet
You mention bass clarinet (I play one). If you look at Dorico’s bass clarinets options, there are actually six. From (my) memory, some German scores have bass clef for the part? and scores can be in bass clef.
If I am notating a bass clarinet part for my own purposes, I always have it in bass clef, it just makes more sense to me that way.
Aside: it’s also nice to play/attempt the Bach cello suites from a cello part (although I have always wondered about the possibility of using multiphonics for the double and quad stops! I’m not that good to attempt it!)
Great bass Dorico instrument
Lowest note sounding C3, written C2.
with part and score octave transpose, bass clef (8 above.)
Normally I would use the standard bass clef (no 8 above) for the part.
There are two factors at play so to speak here, how you might like to input the GB notes, at pitch or transposed octave, treble clef etc; then how you want to export the score for the conductor (which might be different).
Personally if my recorders are playing “chords” together, given the small range needed for this, for Great Bass I normally set the instrument at pitch (non-transposing octave) in the concert score, as I usually build up from there as that is my note foundation at pitch; whereas for contrapuntal lines I might set it as bass clef 8 above (octave transpose) for inputting as I am more likely to go up further in the range.
Another link you might like Arranging for recorder (Sarah again) (if you have not found it already)
Brass instrument clefs you mentioned.
There are different brass instrument conventions for clef depending on whether it is brass band or orchestral, right?
(I think I have all the above as I intend it to say, without any mistakes, I might have to come back and edit something!)