Haplogroup E is also high in Bedouins and northern Arabians.

Which E? You'll find certain E branches Arabians because they are in close proximity to Eastern Africa because E1b1b originated there, so naturally there is geneflow. E1b1b1b (E-M81) and its sub-clade E-M183 are dominate in North West Africa, and we know that the presence in E-M81 predated the Arab conquest. I know you'll also want to mention that J2 as possibility, but research shows that J2 in north-west africa is rare, and that this J2 is a remnant of the Phoenicians. Here is one study: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2668035/ and there is also another more recent one that found the same thing. I'm having trouble finding it though.

Secondly, the figures for Tunisia are over 30% and the figures for Algeria over 20%.

I haven't seen 30% and as of late recent studies have been pretty consistent. The ones that you're referring to from 2004 are outliers.

So I'll amend my statement and say that nearly half of Tunisians and over a third of Algerians have direct paternal ancestry from the middle East.

Nearly half? I still don't understand how you come to these figures. You're just making them up and the data is not there to support that at all. Algeria and Tunisia are both closer to 1/5 than 1/2 or 1/3. You're greatly exaggerating the numbers and studies don't support your conclusions at all. This is merely your opinion.

Either way, I doubt that anything I say will convince you of anything, but facts are facts.