Glad to hear you are operational. I think we can offer better advice if we knew a bit more about how your system was/is wired.
Where are the batteries relative to the inverter, how are they charged, are they used for anything else (house loads, starting, electronics)?
You description of your problem makes it sound like your inverter was completely free standing, that is it was not hooked into shorepower/generator? Therefor power was not passed through when the genny or shore was in use? (This is unusual, given the use of a Link 2000 indicates one of Xantrex' better inverters was being used). Or was it, and the internal transfer switch is no longer operational?
If we had the model of the old inverter, that would help; the fact that you referred to it as a "Link 2000" inverter was confusing, since a Link 2000 is a remote control and battery monitor, not an inverter.
I know you consider yourself to be an expert, but a great way to understand these type marine systems is to pick up a copy of Nigel Calder's "Boat Owner's Mechanical and Electrical Manual". He goes into the whole business of inverters, batteries, charging systems clearly and in detail. Plus there is a plethora of good information about everything else on your boat beyond the electrical system that you will find invaluable.
I think you will find that the electrical issues on the boat are a bit different than the space shuttle or cars or houses. Just my guess, based on my own experience (I come from the electronics business) and that of many other cruisers including electrical engineers. Your Mileage May Vary (YMMV) as they say...
"There's the Right Way, the Wrong Way, and what some guy says he's gotten away with"