I am not sure about noise induced in the other circuitry in one of my homemade multi output units (although it's not been an issue) but I designed the unit to provide somewhat greater than one amp output on 6.3V 5V and 1.25V with fairly small heatsinks. I just sat them on top a fan providing constant cooling. It has seemed to have worked Ok as the unit does what I ask. Not quite as far as you are going, but seems to readily provide well over one amp at 6.3V indefinatly and copes with short lived surges well. The biggest problem I get with linear regulators seems to be the input / output differential putting up dissipation. I have used tandem circuits to reduce this but it starts to get hard work and is obviously inefficient. This is seldom too much of an issue though. When I mount the components close they seem to work without problem. Just overdesign for current flow. If trying to go as far as you I would probably use a heatsink which works well with fan cooling, although my tendency these days is to go with switch mode units I have to hand and apply extra smoothing etc if required. I have also implemented smaller local regulators for individual stages to split the problem a bit. I remember I do have a LM338 circuit for power to higher current valve heaters (usually powered from a good 12V swith mode unit). It does run 2.5A Ok if I remember although is still heatsink limited if left running for any thing over a few miniutes (external heatsink so I gauge limits by hand).
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