Some qpAdm models for Levänluhta

[Jaska]

1. Indo-European languages were spoken on such a wide range at the time the loanwords were introduced to Uralic that placing them to specifically the Urals isn't necessary
Especially considering the only realistic options are extinct branches of Indo-European, Indo-Iranian or Tocharian languages.
2. Languages can also emerge within a larger area and then become the only extant member of the previous language family, which is what happened with Yeniseian languages. Same could have happened with Proto-Uralic, forming out of a larger group of which only it remains.
3. Consider the modern language distributions of Siberia. Evenk is spoken from Krasnoyarsk oblast to the Amur basin. And this has persisted for hundreds of years. And again I'm not saying the language didn't disintegrate multiple times before becoming the immediate finaly Proto-Uralic form, but I doubt it was restricted to a single region with no Para-Uralic relatives around for thousands of years either
4. Calling Sami hunter-gatherers is kind of dubious especially in the 16th-17th century. And consider that the region used to stretch all the way to Dvina Karelia and persisted for two thousand years or so. Even so, Lapland is quite large in on itself, with moder Sapmi being aroun 400 000 km2

1. Of course we are not talking about ALL Indo-European languages, but only about those which were in contact with Uralic. Relevant branches are Indo-Iranian (> Proto-Iranian) and Northwest Indo-European (> Pre-Germanic, Balto-Slavic). These branches were located in European Russia, before ca. 2000 BCE Indo-Iranian spread wider to Siberia and Central Asia. So far plausible Pre-Proto-Tocharian contacts concern only Samoyedic. 

2. You still have misunderstood it. All languages are born in a narrow area, and their expansion to a wider area is only secondary. When language spreads to a wider area, it also disintegrates/diverges: daughter dialects/languages are born (likewise in a narrow area). All widespread languages and language families have begun their expansion from a narrow homeland, that is a fact you cannot escape. 

If only one daughter language survives, it becomes the new proto-language. It also was born in a narrow area, and its expansion to a wider area is a secondary process. And when it spreads, it begins to disintegrate and new daughter languages are born in a narrow area, and so on. 

3. Evenk and all the other languages of the world with a wide region were always born in a narrow area.

Naturally there must have been Para-Uralic languages at some point in somewhere, because every human language lineage goes back hundreds of thousands of years. However, this has no impact on the location of Late Proto-Uralic. It would be relevant only for the location of distant Pre-Proto-Uralic, from which both lineages descend (Proto-Uralic and Para-Uralic). 

4. There is nothing dubious to point out known historical examples, just the opposite: it is paramount to understand that linguistic laws were in ancient times just the same they were in historical times and still are today.

It is true that the Saami region was at its largest from Atlantic coast of Norway to Archangel Region and from Southern Finland to the Arctic coast. Still, all this expanse was again secondary: Late Proto-Saami was spoken in a narrow region in Southern Finland, until it disintegrated ca. 200 CE. Different Saami proto-dialects spread to different directions, and in new wide region always new Saami dialects/languages were born - once again in a narrow region, before they began their secondary spread.

[Norfern-Ostrobothnian]

I'm more interested in the location of Pre-Proto-Uralic rather than the Late Proto-Uralic personally, but even then LPU would have been able to intermingle with Andronovo culture and what not in Kazakhstan and Siberia or even the Sayan mountains.

[Jaska]

I'm more interested in the location of Pre-Proto-Uralic rather than the Late Proto-Uralic personally, but even then LPU would have been able to intermingle with Andronovo culture and what not in Kazakhstan and Siberia or even the Sayan mountains.

Pre-Proto-Uralic is vague, because there is no conclusive evidence but only contradicting evidence: it could have been in Europe close to Indo-European, but it could have been in Siberia close to those language families. So distant past might be beyond our reach forever.

Andronovo is later than LPU, but it probably had some contacts with Siberian Uralic. It depends if it can be associated with Iranian, which was spoken on both sides of the Urals for a long time. Andronovo language could also have been Indo-Aryan or some extinct Indo-Iranian branch.