What is known for sure is only that Albanian and Romanian share many words of unknown origin and that those words have been borrowed between the ancestors of the two languages at an early stage, e.g. before rhotacism has changed them.
However in most cases it is impossible to determine which was the direction of borrowing and there is no evidence to relate them with any of the languages named by ancient historians, because too little has been preserved of those.
Also, there is very little evidence, perhaps none, that the Thracian language and the Dacian were closely related languages. The toponyms that are assumed to come from these two languages are not similar.
The supposition that they are closely related is based almost only on the claim of Herodotus that the latter were a tribe belonging to the former, but that claim might have been based only on similarities in clothes and weapons, even without related languages.
Again, recent work has established the direction of borrowing for many items as Albanian > Romanian due to secure Indo-European etymologies for some of the Albanian material. And for certain other items, recently it has been proposed that the direction is dialectal Latin > Albanian, undercutting any claim to Dacian origins. You are right that little is preserved of certain ancient Balkans languages, but there is enough preserved in toponymy and onomastics in order to establish affiliations based on the reflexes of the PIE velar series and the vocalism. That is what, in the last 30 years or so of scholarship, has excluded Illyrian and Thracian from playing any role in the Albanian–Romanian lexical isoglosses.
Matzinger himself provides a single example of a word for which there is no doubt that the direction of borrowing was from Proto-Albanian to Romanian ("thark").
For other examples, he sends the reader to a work published by Stefan Schumacher in 2009, which I neither have nor can find online.
Perhaps you know the title or some link toward any of the recent work that you have mentioned, about these words shared by Albanian and Romanian.
While for the shared words of non-Latin origin it may be that most have been borrowed from Proto-Albanian to Proto-Romanian, the shared words of Latin origin may have been very well borrowed from Proto-Romanian to Proto-Albanian.
We cannot know if there has been any descendence relationship between the speakers of Latin from whom the speakers of Proto-Albanian have borrowed words and the current speakers of Romanian, but we also cannot know whether the contrary is true.
For Indo-European etymologies of some other Albanian words shared with Romanian, look to the work of Eric Hamp: off the top of my head I can list his IE etymologies for the Albanian counterparts of Romanian vatră, strungă, and bunget that seem generally accepted. Getting up to speed with Hamp’s work will likely require some travel on your part, because Hamp tended to publish squibs in some fairly obscure collections and Festschriften that are only held by a handful of libraries and are not online. Orel’s IE etymology for the Albanian counterpart of Ro. zară is, I believe, the current consensus.
> The shared words of Latin origin may have been very well borrowed from Proto-Romanian to Proto-Albanian.
Yes, certainly. But if those Proto-Romanian words can be shown to represent dialectal Latin features that came to the Balkans from outside, then there is no case for a Dacian origin for them. Dan Ungureanu has argued this recently for a number of items, and a few of my colleagues working with these languages think this represents a great contribution.
I agree than despite traditional claims, there is no known relationship between Dacian and any of the words shared by Albanian and Romanian.
Unfortunately, Dacian is likely to remain one of the least known ancient languages. While for Thracian there has been some small recent progress and it seems that it might have been more closely related to Phrygian and Greek than previously believed, for Dacian it is unlikely that there will be any future discovery of inscriptions that could provide extra information.
However in most cases it is impossible to determine which was the direction of borrowing and there is no evidence to relate them with any of the languages named by ancient historians, because too little has been preserved of those.
Also, there is very little evidence, perhaps none, that the Thracian language and the Dacian were closely related languages. The toponyms that are assumed to come from these two languages are not similar.
The supposition that they are closely related is based almost only on the claim of Herodotus that the latter were a tribe belonging to the former, but that claim might have been based only on similarities in clothes and weapons, even without related languages.