I would avoid changing government twice, unless perhaps you are playing a religious civ. Even as a religious civ, it usually isn't necessary to change twice. Just make for Republic, and change when you get there. Avoid self-researching the religious arm of the tech tree. The AI will do that for you. You can begin your first expansionist war before you even get to Republic in many games.
Republic does give War Weariness, but you avoid that by being tactically smart and diplomatically aware. Avoid letting AI units attack you. Instead, attack them first. You don't get WW points for attacking and winning. Of course, sometimes, you can't avoid being attacked, so in that case, make sure your defense is good enough to win. You build WW points for dying in combat, so don't lose units. Most crucial, of course, is don't lose cities. One fallen town is equivalent to roughly ten lost units for WW. As for the diplomatic part, when WW does kick in, make peace. Be sure to extract soemthing of value. WW is on a per-civ basis, so if you want to, you can attack Civ 2 for the 20 turns that peace is in effect with Civ 1. At that point, WW versus Civ 1 is reset, so you can go back to beating up on Civ 1. This is known as Oscillating War, and it is a very effective way to win territory and keep up in tech as a Republic.
In the high middle ages, I sometimes find that, as you say, my war machine bogs down. That's OK. Set the research slider on high and spend a few turns building units. I like to beeline for cavalry on the tech tree, and spend some time building knights. When I get to cavalry, I cash upgrade, and my war machine is once again able to shift into high gear.