There are quite a few anti-strategic methods you can use. One of my most favorite, and if not the most effective thing I have discovered in this game, is a two-stage system.
Instead of using one group of units to attack, you use two. The front line do NOT move and simply defend. The back line advances and becomes the front line next day. Repeat with the new back line. This does;
1) If your enemy is someone who waits until the last moment, this works to your advantage IF;
1a) during the daily cycle, countries are randomly selected to move. Your enemy goes first and get demolished by the front line who have a slight defensive advantage. You go second and your back line moves forward practically uncontested.
1b) You go first, your back line advances and may die or not. Your enemy then move his units. He expects to be attacking your front line (which is now the back line!) and may have his attacks failing due to your new line of units defending.
2) If your enemy is someone who does not care about the daily cycle and just create his units and attack routes at any given time he is able to log on, this works to your advantage IF;
2a) You choose to wait until the last minute, create units in the "back line" and use them to attack, while using old units as a front line. The front line do not attack and defend. You end up going first, your back line advances and clash. Any air attacks he make will most likely be shot at by your new front line, since the attack paths likely are targeting your now back line.
2b) He ends up going first, luckily for you, your freshly created units is a surprise to him and he gets demolished. Your units then advance almost uncontested. You will, however, lose your front line.
You can even make it perfect by creating three or four lines of defense, using only 1-3 lines to advance and 1-3 lines to defend.
Don't forget, it's largely balanced by having countries randomly selected to go first or second or fifth or so on. Certain methods work best if you go first, others work best if you go second.
What would you recommend, if anything, to replace the daily cycles? Having it at different times is moot, as people live around the globe. A certain time works best for you, but not for me, while a different certain time works best for me, but not for you.