Martell Knights

You'll have an easier time with setup and getting characters on the board if you don't play so many duplicates of unique characters: I would do 1X Darkstar, Arys, Barristan, Mandon Moore, Meryn Trant, Boros Blount. 2X Jaime & Preston. That will give you more room for 3X non-uniques.

A good rule of thumb is that out of ~30 characters, no more than 50% should be cost 3+. You have 19/33, that seems high. 3X Hedge Knights to replace some of the removed duplicates would help your gold curve.

Myr 1X. You have 9 limited cards, that's a bit high. With so many shadows and neutral cards, I would probably focus on gold rather than reducers. 3X Water Garden, 1X Roseroad, no Twilight Markets or Palace Fountains. That plus 2X Fiefdoms should be OK. Now that Red Keep is restricted you could replace it with a Kingsroad Fiefdom, but that still only gives you 6 influence. If you want the influence just for Red Vengeance, I'd suggest dropping it and playing Viper's Rage instead.

I agree with most of the advice above - with the restricted list changing you now have to choose between Burning on the Sands and Preston. I would try Preston to begin with (he works so well with the rest of the KG). The other recent change means you should seriously consider getting the chapter pack containing the refugees (Refugees of War) as these guys are 0 cost for 2 strength.

Given the deck relies on summer a fair amount I would also look to include some Carrion Birds.

On plots, Building Season is generally not a good idea in joust. You are allowing your opponent to find the location they want. Whilst you also get the benefits, there is a chance they will have a more crucial location than you (you really don't want to give Lannister the Iron Throne or Targ Aegon's Hill for example). If you have the pack (A Song of Silence) then Retaliation is a great plot to replace it. If not, A song of Summer provides good gold and initiative with a chance of a benefit too.

To replace Burning on the sands is difficult. The following events are all good (none directly replace its effect though)

He Calls It Thinking - One of the best cancels in the game, I find it very hard not to include 3 in any Martell deck.
Blood for Blood
Muster

Choosing the Spear is also great - but again you will need to buy a pack for it.

The other recent change means you should seriously consider getting the chapter pack containing the refugees (Scattered armies) as these guys are 0 cost for 2 strength.

*cough* Refugees of War.... *cough*

Edited above!