As with any good game there are actualy many valid methods to finish something successfully.
The above is a good way to play the map through quickly (and may not be a bad idea to have 1 or 2 units here and there for exploration with the above tactics).
I myself enjoy a long, relaxing, exploritive game. I have found several times that had I played a fast and furious game I would have missed out on some little things (like the spirit of life reward on that map for removing a fire node, which a pioneer can rebuild, on that side island) as well as a spell that can be reached via a teleporter (which interestingly puts you near Yaka's main cities). I also would have missed the elvin city... probobly.
anyway, if you want to play a slow and relaxed approach and also don't want to bother with sending troops back and forth then I sugjest, with that massive gold income, that you build a defensive group to sit on certain key choke points that lead to your heart.
at the main city (near where you started) I put a mixture of 2 knights (probobly could have just used swords men), 2 monks, 2 swashbucklers (you can exchange the 2 knights/swordsmen with 2 more swashbucklers) and 2 cannons/balistas.
That comes to a total of 8 and generaly can slaughter some of the largest attack groups if they have a wall to sit behind. I put these guys in towns and at towers near choke points. for choke points without a tower that I might attack with but not realy move much around (basicaly guarding an area) I had 4 knights, 2 monks, 2 cannons/balistas.
about cannons vs balistas, balistas do fairly well but cannons are better... basicaly if cannons are too expensive/slow to produce then balistas it is. as for the trebuchete (or whatever that is called), it can be quite effective but somehow luck is against me with them. The enemies trebutete almost always hits me but mine almost never hit them reguardless of enchantments or level of units.
Thats basicaly how I play all my maps, I expand out quick to take enough cities/resources to keep me happy (much as you did already) and then slowdown (sorta turtle) and start exploring. Also while exploring I generaly am continuing to upgrade my cities and build a massive attack force. (so gold is almost always low) I try to get one city up to teleporter status and have wizard tower 1 minimum on most of my cities (I go for coverage rather than every single city). That way if I need to deploy troops, they are out fast.
A hint about this tactic is you will want to play the game in simultanious on maps with 2 or more AI unless you have a fast system and even then probobly still. This tactic tends to allow the ai to continue to build up.
one last note, when defending you are best off controling the battle (saying yes) rather than not becouse FC (fast combat, saying no) gives the attackers the advantage (they only have 1 gate to kill and start out right near it virtualy speaking).
as far as Yaka moving troops back and forth, there ain't much you can do about that. He will push forward if he thinks he can win, and pull back when you change the odds. The only real options (to my mind) are to have troops nearby to retake what was lost if you loose, saturate the areas with troops (expensive!), have fast units to pursue yaka fleeing, or play fast and furious...
Biggest thing, have fun. With time you are bound to find your style