a lot of people scorn soft solder yet it isn't as bad as you make out, bog standard 60/40 solder is strong if the joint is done correctly, if you require additional strength use a 3 % or 5 % silver bearing solder or even Alusol yet at around £36.00 per spool it expensive.
hard solders (silver solders) start at around 610 c and go up to around 820 c anything above this is classed as braze and embraces bronze types gold or palladium type and aluminium, titanium types but wont go into detail here as specialised area.
sticking with silver solders there is no such thing as extra easyflo or easyflo hard well in 25 years dealing with J&M easyflo solders I have NEVER come across them, the most common types are easyflo with 50% silver 15% copper 16% zinc 19% cadmium, or easyflo number 2 with 42% silver 17% copper 16% zinc 25% cadmium, then easyflo number 3 50% silver 15.5% copper 15.5% zinc 16% cadmium 3% nickel.
there are now the cadmium free types these are safer to use due to of course no cadmium slightly higher melt but safer to use common types silver-flo 55 and 60
as for cleaning prior to soldering don't use steel wool microscopic steel particles get caught in the soft material and cause pinpricks to occur in the join and also aid in interfacial corrosion, don't use washing up liquid might be OK with brazing but never silver solders, if soldering aluminium bronze add table salt only a little as the chloride in the salt causes the flux to go into overdrive when heated.
only use brass or stainless steel brushes or wool, emery the joint instead and allways clean well with simply soapy water.
don't quench after soldering this only adds to the annealing simply let it cool naturally, if you want to read more please feel free to have a look at my site
www.hanna-parts.co.uk at the side menu you will see marine and there you will find a topic on soldering from types to tool through to materials for jig construction.
will be moving the site soon so if down when you try it will re appear again once it has Bean moved.