Sorry for the late reply, was hiking in the north.
About 70% of the thru hikers hike in spring. No doubt spring is the best season, it's not just the flower factor, I call it: Green vs. yellow factor, and it relates mainly to the northern part of the INT.
I believe you are an experienced hiker that will come well prepared for the hike, I mean physically. I'd like to suggest a modified plan for your hike:
Start in Arad in mid April. It will take you 2.5-3 weeks to get to Eilat and then take a bus north to Dan and hike south to Arad.
Fall is a more relaxed hike compared to starting in mid April in the north.