In regards to doing deeper testing some of the tests are quite expensive. Big-Y on FTDNA is $499, but it sometimes goes on sale during holidays for as little as $250-300. However since I know some of the admins for L283 I have asked them what would be the cheapest way to determine your terminal SNP, since I know you can test for specific SNPs quite cheaply, and since you know that you would fall somewhere downstream of Z631, maybe there is a way to determine your terminal SNP for less than $100. I will let you know once I get a response.
Regarding the Illyrian question. Yes, the Greeks referred to the barbarians in the North-West as Illyrians, as such it was an umbrella term for people that were related (as tribes, culturally and maybe genetically), but might not have been the same people, similar to how they refered to people in the North East as Thracians, for whom it might have been a similar case.
Right now I am positive L283 was indeed an Illyrian Haplogroup. We find it 4k ypb in Maros, and 3.7k ybp in Dalmatia. And a paper is coming out soon with a Bronze age L283 in North Albania. These dates predate the term Illyrian by maybe more than 1k years. However, given what we know about Illyrians, where they were located, their movement North to South during the period they were identified by the Greeks etc, in my mind there is no doubt given our current evidence that L283 was indeed an Illyrian paternal line during this period.
Regarding Albania, I would say L283 is indeed a dominant line. As in R1B z2103(not I2, think you made a mistake), E-V13, and L283 all make up between 20-30% of Albanian male lines. As such depending on the region any of the clades can be dominant. Meaning there is no meaningful difference in the %tages. There is no point using modern frequencies to determine anything however, ancient samples in the case of L283 are the strongest proof, since modern frequencies can be due to founder effects and bottlenecks.