score:6
TL;DR: All routes you're likely to use are tolerably safe.
Broadly speaking, the insurgency affects only the eastern bits of southern Thailand: Yala, Pattani and Narathiwat. However, all 'standard' backpacker routes from Langkawi to Thailand, including the main train line via Padang Besar, go through the western side, not through any of those provinces.
Hat Yai is targeted because it's the largest city in the South, but then again, Bangkok has also been targeted, although the jury is still out on whether southern insurgents were responsible. Most bombings in Hat Yai have targeted places where Malaysian tourists come to cavort with Thai prostitutes (karaoke bars, rent-by-the-hour hotels, etc), so if you avoid this profile, odds are high you'll be OK. The vast majority of the "daily" attacks mentioned target Thai military and police security forces, not random passersby, much less foreign tourists.
Upvote:4
Very few tourists have been killed or injured during the many years of southern insurgency. The violent acts target security forces (police, soldiers, village volunteers), government officials and school teachers. The tourists that have been injured or killed were all visiting the eastern side of the isthmus. As jpatokal mentioned your route travels up the west side of the Kra Isthmus.
Ultimately you are putting yourself at greater risk by taking a bus, as more civilians (and tourists) are killed in bus crashes each year, than by insurgents. And if you are thinking about renting a scooter, three times as many people are killed in scooter crashes per year than the total number killed by insurgents since 2004.
The risk from insurgents is not something to worry about, other than the usual common sense precautions when traveling.