New cooling system, still overheating.

Wow, sorry to hear about your troubles.

Since you are experiencing rust (have in the past) as an insurance policy, you need to pull radiator and either professionally back flush it or do it yourself.

It would be best to pull your thermostat and back flush your whole motor and cooling system with the radiator out.

Like said above, you can run distilled water but must have an excellent corrosion protection additive designed to run in a water-only system. I am not good at figuring this radiator chemistry stuff out so I run 50/50 pre-mix because it is guaranteed to work in most climates. If your system is prone to rust issues, I would change coolant and flush the system once a year and run full of premix 50/50 and keep a gallon in the trunk incase you need to top it off while you are on the road so you don't have to use tap water.

Since you are prone to having rust issues, also I agree that you need to protect your radiator at all times with a screen on the top hose, or a ganofilter. Here is the ganofilter which may periodically clog with gunk but will prevent the ruining and clogging of your radiator. I suggest the clear one so you can see when it is dirty and clean it out.

http://www.ganofilters.com/


It all sounds like debris and rust is or has clogged your radiator which leads to all your other problems.