I'm not saying that you wont be able to get a perfectly acceptable re-circulation rate, just that it will most likely be, as it is in most re-circulating systems, the limiting factor for temp control, ramp rates and the like. I was painting that as an opportunity for you to simplify your wiring needs - not as a problem. Your second element is basically irrelevant for your temp control system - you are safe to ignore it and make your life easier.
I can see that its possible that a system with a bag as well as a false bottom might perhaps be more prone to issues with the mash not circulating easily because the bag isn't the ideal lautering surface - but thats just something to be on the lookout for, its not that it "will" be a problem, just that its a possibility.
You could use the returned wort to "stir" the mash, and if i were building a BIAB re-circulating system, a way to do that would be part of my design... But i am NOT saying that i think its necessary for you to build a successful re-circing BIAB.
As a born and bred BIABer - you need to remember that the bag is NOT part of the mashing process, in normal BIAB, the bag is, or at least should be, entirely irrelevant to the mashing part of brewing, it should only come into play during lautering (ie when you pull the bag out). What you are doing with your re-circulation, is ALL about the mashing process, and basically nothing to do with BIAB. Read the threads about HERMS and RIMS brewing - they will be much more use to you than the BIAB threads. You suddenly need to understand mash tuns, you are about to build one. For re-circulation, flow rate matters, a lot. Think about it in your system design.
That auberins PID - sorry, i dont know. It says it has a "manual control" mode... But whether that means what we are talking about or not I dont know. You will have to discuss it with the seller/manufacturer, or perhaps someone from AHB who has one can let you know. I just wanted you to be aware that not all PIDs are able to control that way and make sure your's could if you needed it too.
Regardless of that, i would be inclined to run with two elements rather than one big one. This (probably) gives you a lower watts per square cm ratio - and thats a good thing for use in brewing. Also the elements from craftbrewer are nice smooth, easy to clean, stainless units - you will be able to clean them off with a quick wipe with a rag, no twists, bends etc to worry about. While the bigger units are normally water heater elements and are generally a bit more convoluted.
Me personally - I wouldn't build a system with these sorts of elements at all - I would do this
http://www.aussiehomebrewer.com/forum/inde...mp;#entry741566
Or some variation thereabouts, with a bog standard 2400W over the side element to add a little grunt to the situation when heating your strike water or trying to get to the boil. You only have a 50L pot, so i am assuming you are planning on single BIAB batches. Those crown elements are proven to hold a sufficient boil for single batches, so no need for control of the element during the boil, no extra installation or wiring for a "second" element & those elements seem almost perfect for installation under a false bottom. You also, by building a system like that, happen to be building a perfectly serviceable RIMS mash/lauter tun. So if you ever decide to to go 3V - all you do is take the bag out and add a kettle and HLT... No mods required for the mashtun/RIMS whatsoever.
There are bunch of different things that can and will work - just dont get too stuck in the BIAB paradigm for this build, its only partially applicable. Look at what you want, why you want it - and at what other people have done in similar situations. You really aren't doing anything new here, no need to re-invent the wheel.
TB