Back when I was trying to decide on WHICH alarm to get from JLC, and before I found out I could get the TTP 65 (indeed, the last one!), I thought about trading in my EWC for the EWA. It was a momentary flirtation and a foolish thought.
The EWC is such a phenomenal piece, and for me was and is a much better option than the EWA, even though that Tides of Time is a beautiful rendition of the EWA. The power reserve of 65-72 hours is really nice if you are rotating watches. The chronograph/world time is such a nice, relatively rare, and useful combination, and I would miss having the chronograph (would you?) function. Side by side, I have a clear preference for the design and overall look of the EWC over the EWA.
I don't argue your idea of creating a JLC alarm collection, but as Nicolas has already listed above, there are a number of Memovoxes to collect that you don't really need to get the EWA unless yu are truly going for a complete collection (in which case, GOOD LUCK with that). I think I would choose a number of JLC alarms over the Tides of Time -- again, just IMHO -- the MC memo, the International, the Tributes to Polaris, the new DSA Tributes, and that doesn't begin to cover all the modern or the vintage pieces.
Now if I were just going to get ONE alarm from JLC and just ONE MC Extreme watch, I could make a great case for the Tides of Time covering both bases. But it sounds like you will have more than one in the end. In a collection that includes several JLCs, I could live without the EWA. But I have had a hard time imagining being without the EWC.
Take all of the above with a grain of salt, as I am one of the EWC's biggest fans, although I realize PeaceFrog gives me a run for my money. ;-)
Good luck with your decisions.
respo