Everything you wanted to know about voller vs voll and will probably regret asking by the time you've read this whole thing. (I know I did)
The short answer to your question, as opposed to what follows below:
The distinction between voll and voller is the result of habit and changes in language use, and its origins keep academics busy writing paper. If you want to offer a definite answer, don’t use SE but write academic papers instead!
If you want a longer answer, a whole analysis even, from actual German professionals in linguistics, have a look at this:
Zur Wortart und Kasusrektion des Wortes voller
That’s right, a linguist actually held a whole presentation on the word voller vs voll and its development! And he quotes other linguists who apparently have discussed this.
The paper discusses a number of issues with the word voller.
It starts with some examples, similar to your original question in showing how voller is used (instead of voll), with special focus on its frequent colloquial use
voller erscheint ziemlich harmlos, alltäglich: [sources removed]
- außerdem ist die Schere voller Klebstoff
- dunkle Wälder voller Zombies
Wird früh erworben: (… 6-jähriger)
(Papa kauft die Wiener Straße in Monopoly)
du kriegst da umsonst wiener würstchen [sic!] oder is da alles um nur voller Metzger
voller appears to be harmless and common:
- The scissors are covered in [full of] glue
- The woods are full of zombies
It’s acquired young in life [quoting a 6-year old child] (father
acquires the Wiener Street in [the German version of] Monopoly
… du you get Wiener/Viennese sausages for free there or is it all
full of butchers?
Then tries to determine what kind of word voller is
- […] Was für einen Kasus hat Klebstoff? Zombies? Metzger?
- […] Was für eine Phrase kann da sonst stehen?
- […] Was für eine Wortart hat voller selbst?
- [In this context] what case do glue, zombies or butchers have?
- What else are you going to use?
- Just what type of word if voller itself here?
This goes on for slide after slide, quite mindboggling really.
I’m just going to nitpick, because it’s a quiet Monday at work for a change.
I’ll translate without the original German quote to keep this (somewhat) short.
There is one theory of the history of the word and how it developed out of voll:
A common theory derives voller from voll der
This, as a result of
sloppy pronunciation and where use of the article seemed
voll der Gnade -> voller Gnade
But that theory seems to be no longer held. Now they call it a
erstarrtes starkes masculines Adjektiv
a crystallised strong masculine adjective
Really! That’s what it says!
Which puts it in the same category as word like selber and halber.
What case is it and what case is it used with?
They don’t know:
It’s not genitive: eine Flasche voller Wein
It’s not dative: eine Stadt voller Kinder
Leaving accusative or nominative. Except sometimes you don’t know.
There’s some quotes from people on German-English forums asking questions (not Stackexchange though ;)), essentially the same as yours:
Q: Is it correct to write Eine Badewanne voller warmen Wassers?
A: Not sure, I’d write Eine Badewanne voll mit warmem Wasser, but
without the article I’d write Eine Badewanne voller Wasser.
There’s even suggestions that voller is wrong and should always be avoided in favour of voll. So instead of
Das Fass ist voller Wein.
Das Fass ist voll.
Das Fass ist voll mit Wein.
Das Fass ist voll Weines.
I got to about slide 20-something (and that cherry-picking) out of 40, before I went “you’ve got to be kidding me!”
So, here’s the author’s summary
dependent on a network of other constructions