You are almost decribing what i've seen before with master cylinders needing overhaul (''sinking feeling''), but i'd leave that alone for the time being, possibly a servo problem?
Full brake strip out if not already done, clean and check everything, coppaslip pads and any caliper sliders, grease pistons after pumping them out a little, reassemble and flush through with fresh fluid....that would be my way forward for starters.
I'm assuming you have discs all round, if you have rear drums are the slaves ok?
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