If the hoses have become spongy and soft someone has used the wrong coolant or an additive of some sort along the way. Based on your findings (good job btw) sounds like a classic case of a plugged core or an air bubble. I vaguely recall the focus using an outlet restrictor to reduce noise through the heater core but I'm not positive this is the case. Another reason why small floaties could have plugged you up.
These don't seem to be hard to burp - my SVT has been drained several times and had a thermo housing replaced and I've never had trouble getting bubbles out... the degas bottle is the highest point in the system so it works as designed (unlike Windstars, cobra mustangs, navigators, aviators, etc) so my money is on a plugged core especially given the color/condition of it as you found.
The pressure leak will only cause you to lose coolant - it shouldn't affect the cooling ability of the engine or the heating ability unless it's literally running out.
Backflushing a foci heater core looks like a bitch but I'd say it's the only thing worth your while at this point
All gold coolants are not created equal. Just read the bottle carefully but you want coolant with nitrtite additives. Universal coolant is b.s.