When should I submit a warrant officer packet?

Generally I would say make staff first. Warrants are experts in their field and no matter your intelligence level, 3 years does not get you that status. Once you have done both strategic and tactical assignments, them I would say it's time.

I submitted and was accepted at the March board this year, and I leave in a week for WOCS. I must admit, I feel like I waited too long. I wish I had made the decision a few years ago. I think 8-10 years in service, E6, is about right. I am at 14 years, with three years as a SFC. I think I will be among the 'crustiest' NCOs at WOCS. I waited because I wanted to be highly experienced in my field (35P), and by the time I was ready, my MOS didn't exist for Warrants anymore. I struggled to become a 3+ in my language and qualify in multiple dialects, get a degree in my field (ME Studies), and do multiple overseas tours- but now my language skills aren't even a requirement for my job.

5 years in, with 3 years of experience is a little early. I think it's best if you have at least done both strategic and tactical tours, and an instructor or TRADOC tour would be great on top of that.

My experience may be a bit dated but, that said, it can never hurt to submit a package --- worst case, you don't get it and you try again the next time.