If you want an exploit to really kick their ass, here it is in one word.... 'escort'

The reason... the AI will target any escort class ship first in battle.

So all you need to do is have one escort class ship with minimal weapons but lots of defense. All your other ships, even tiny ones, set to 'capital'.

When to switch to war economy is going to vary a lot with how big you seem compared to others and a lot of other variables.  It is going to vary according to your map choices and playstyle.  Therefore, it is difficult to give you a pre-planned schedule.  I suggest playing a couple games with a deliberately weak military build up.   Take note of when the enemy factions start getting noticeably belligerent and threatening.  You should be able to notice their tone changing and getting more aggressive.  Then they will declare war.  That is when you take careful note of the turn number.  That is a key data point.  After a couple of games, you should get a good feel of where that number lies.  Start thinking about how many turns it takes you to research military techs and actually start building war ships.  That gives you an idea of lead time needed.  If you put together those two pieces of information, you should get a good idea of what your personal basic strategy schedule is.  "I should start now or it may be too late."  It is no guarantee.  The AI does things on different schedules in different games and you will have to adjust, but it should give you a good start on keeping ahead of those villainous monsters out there.

One thing that is a huge problem with the Iconians, is that their ships repair in combat.  This makes fighting them very difficult.  The tech required to do so (versus for other factions) is incredibly low on the tech tree, and doesn't require ship modules (modules that are added actually are far less effective).

I actually started to prefer playing custom-races with the Iconian tech tree just for this bonus, which combined with combat attributes (hit points and jamming) becomes incredibly effective.

Escort is not always first, but it is always before capital and support, these are charted out for convenient study in the wiki.

http://galciv3.gamepedia.com/Ship_roles#Ship_roles

As it shows, escorts also start closer to the enemy than capitals.

My post in this thread should be helpful to you, if you're losing on easy, you're probably suffering from many of the same problems I documented in the guy's save file.  The game is a bit counter intuitive when it comes to planet bonuses, and there seems to be a tendency to try and maximize them in a way that utterly cripples the maximum output of a planet.

You don't actually need to do such things to be even with the AI at normal, it doesn't do them itself to any significant degree, so matching their non cheating performance isn't nearly that difficult.  It's at higher levels that really taking care to maximize each planet becomes more and more important.  Fine tuning the pop/production percentages to maximize your raw to output conversion will be quite a bit of math, but unless you plan on playing against super cheat crazy AI, all you'll really need to do is pop out a few farms and spam a single type of production for each planet.  Just know that it's possible to have crazy powerful planets that pop out huge hull dreadnoughts in a couple turns with the right building combinations on the right high end planets.