I tried 5-3-1 but really could not stick with it long enough to notice anything. It is very tough for me to stick with a program that goes beyond 10-12 weeks. I like to test a lot of the stuff I give to clients before hand, and I also want to try a lot of different ones from various domains (Football training, Rugby, Strength and Conditioning, Crossfit, Oly Weightlifting, Gymnastics, Powerlifting, Bodybuilding, Weight loss, muscle endurance, etc), to increases my knowledge.
My opinion from trying it is for you to benefit from it, you'd have to stick to it for a very long time. The downfall, as you pointed out, you aren't going really heavy too often.
I have tried it on a newbie, but I switched her on to conjugate after a short cycle. When you're a newbie, you can hit PRs every other week, so you can really just do a weekly progressive loading and you'll likely hit decent PRs fast. On 5-3-1, she was lifting too light too often.
Maybe you can switch to something else.