"For one, do I need a second one configured as LVD"
Yes.
No matter which controller you use, there will be a 'second controller' in it if it also does LVD.
And 11.9V is generally considered 'dead', though it depends on the load and battery capacity.
That 10.5V thing is to keep from ruining the battery or inverter the first time it goes too low.
"As for the dump controller, what kind of current can it handle?"
My controller? Practically infinite.
Just keep adding individual fets and individual loads.
There is a time or power when a full-blown bells&whistles controller makes more sense.
"can it trigger a relay that would control a bigger current?"
Sure.
Two choices:
Make it slow and sloppy and not much of a controller.
Or
Let it be accurate like was intended.
"And what's wrong with relays?"
They require making it slow and sloppy and not much of a controller.
OR
The relay beats itself to death in a Very short time.
Standard $3 car relays are rated for 40A? And ebay stuff is rated in 40A increments?
Some of those controllers offer extra car relays to expand capacity?
Some offer extra-fancy 50A relays.
In short, a relay is designed to operate slow enough to see, and maybe only 2-3-10 times per Minute. Some more.
Factory controllers like the TS-60 operate at 300 times per Second. (the 110V in your wall sockets only operate at 60 times per second).
And 300Hz is 18,000 times a minute.
'Bring a knife to a gun fight'? Relays are like bringing curse words and angry looking eye contact to a gun fight.
"with your controller I would need 1 blocking diode for each generator,"
Yes, like any controller.
"but just one controller on the battery bank"
Yes, like any decent controller.
I am NOT saying my controller is the best for a 60A system, and I am saying something from a Known Name Brand with bells&whistles is often better.
I AM saying a majority of the name brands only available on ebay or their own personal website is inferior to something with a real name brand.
Some of that stuff does more harm than good.
G-