Given that I doubt you can fly direct MCI-LHR anyway, the fact that you've found MCI-EWR-DUB as a one-connection flight seems better logistically anway.

But yes, I do agree that you have to either have all your flights connected on the same itenerary, or "pad" the timing greatly (like at least a day between connections) otherwise.

Meanwhile, here's a strategy for United miles:

1. Apply for the Chase UA Explorer card under the best offer you can find.

2. Apply for the Chase Freedom card under the best offer you can find. Then use it on its rotatng categories (and presumably nothing else after you do whatever spend is needed for the signup bonus). You end up with tens of thousands of Ultimate Rewareds (UR) points, which at that moment can't help you a bit, but hold on to them. (This card has no annual fee, so it doesn't hurt to keep it "forever" and just always use it for its rotating categories.)

3. Later, apply for the Chase Sapphire Preferred card under the best offer you can find.

One you ahve the Chase Sapphire Preferred card (which also earns UR points), you can transfer all the UR points you've earned (including the ones you earned on Freedom) to UA!

However, this card has an annual fee (after the initial year), so you may not want to keep it. That's why you want to wait and get it last, because it "unlocks" the Freedom UR points you're able to earn before you get it, and it costs nothing the first year.

(The UA card also has an annual fee after the first year, but it comes with travel benefits like early boarding and free first checked bag and a couple lounge passes, while the Chase Sapphire Preferred doesn't. So if you only want to keep one card that has an annual fee, of these, the UA might make more sense.)