This is a fun concept and I'd like to take a run at it.
If I'm named general manager TODAY, now hypothetical going back in time, etc, here's what I would do to set the Eagles up for long-term success.
Also, I'm acknowledging in this thread that as a GM I don't set the budget, so I'm not going to pretend that the way to go is acquiring top 10 picks that don't want to play on the Island.
The two main philosophies I think that need to be adopted to bring the Eagles success are
1) Player development - The most important thing a small market team can do is properly develop drafted players. Give them ice time or leave them in QMAAA for another year, whatever you need, just hit on your picks, develop talent from within.
2) "STOP SCREWING WITH IT" - This is a fun little term that means "follow the process". I think the biggest frustration for fans, reading comments here, really comes down to screwing with the process. Moving off players too early, trading high picks for veterans in years when you're not going to contend, this is "screwing with it".
In a vacuum, the Eagles situation right now is not bad. You have a 1st and 4 2nds going into next year.
I think you just hold your training camp, and put a premium on developing guys like Sheilds, Richard, and Foley up front.
At the Christmas trade deadline, I honestly think you still stick to the "Don't screw with it" philosophy. You listen for offers on guys like MacDonald, Boutin, Houde, Newcombe, Biggar, Smith or Ruccia, but you acknowledge your pool of picks is pretty strong and you're not desperate for assets. If someone wants to make a trade, make them make a good offer. Stop taking pennies for the dollar on players. (And just as importantly, stop paying premiums for guys you don't really need.)
I honestly think that with just a bit of patience, proper drafting and development, and a few shrewd moves the Eagles could be good again as early as next season, and extremely competitive the season after while still having assets in the bank and young players in the system.