Studio lighting - white background - HELP!!

Apologies for the long message - thought if I give as much detail as I can it might help you help me!

This is driving me nuts to be honest. I've been doing home studio shoots for a while now and for the most part I've been doing OK with improving results, but to be honest I think a lot of this has been through trial and error than anything else. What I want to understand is how I can get consistent results with properly exposed subject(s) and a pure white background.

I have a three light set up, I use either a softbox or a brolly shoot-thru on a 600W strobe. Then I have two 400W strobes at 45 degrees onto either a 1.35m wide white paper roll if it's just one or two subjects or a white cloth background if I need more width. These either have a spill-kill on them or sometimes I use a bare bulb approach with a white piece of card acting as a goby/flag thing on each one.

Anyway last weekend I set this up at my parents house and did a shoot for my parents and my sister-and-family. Things looked OK on the camera screen (don't they always?) but when I got home and uploaded the shots they were all washed out and over exposed and it seemed to me that perhaps I was getting a lot of light reflection off the (cloth) backdrop. I had whacked the backdrop lights right up to max because it seemed that was the only way I could get the background to blink entirely. I think I also pushed it to ISO250 for the same reason.

So having read up on this and watched one or two videos about it, the suggestion is I really need to be metering my subject and my backdrop more accurately. So today I set the lights up at home, had her three or four feet in front of the backdrop, metered her at 1/160sec f/11 ISO100 (using handheld light meter with the key light). Then I metered the backdrop and it was same but f/16. Two stops difference as has been suggested.

And the results were not quite what I wanted. The backdrop was shown 'blinking' in places, but certainly not all over. I moved the light angles around a fair bit but not much improvement. I had both 400W lights at about the same setting strength wise.

What I didn't want to do was push the lights too far - once I did that I was metering f18+. And the purpose of the experiment was to find out what I needed to do to get things "accurate" and properly exposed.

The other thing I seem to be getting is that on the right hand side the light seems to be slightly less than on the left? I did wonder if my cheap-came-with-the-lights wireless trigger was the issue so I also tried with a cable. Same result. The strobes themselves are supposedly pro-quality ones - certainly not a budget set. I'm sure they do the job, it's this idiot with the camera who need the help!

Any advice? What I want is nice well exposed subject, clean white background that doesn't need 'shopping to clean it up (at least not too much), and no bounce-back from the backdrop to affect the subject.

Attached is a shot I did today with the results I'm on about (no photoshopping, just converted from RAW to JPEG). Now I can sort these things out in photoshop, sure but it's not what I'm after. At least my show-off-daughter-model is exposed pretty well, but, well, meh....

Thanks for your time/advice/shoulder-to-cry-on/food-parcels.