Hm, I think you both could have shaved a couple minutes off by just going through security in T1 instead of walking over to T2. once you're in there's a passage over to T2 and out emerges close to the gates. I think that's a slightly shorter party though whether it saves time might depend on the relative lengths of the security queues.

Also, for what it's worth, US airlines are a lot more forgiving about such matters than European airlines. If you had missed the UA flight but presented yourself at the checkin deal within an hour or two (I forget the policy) they would have accommodated you at no charge. The next flight might not have been for a few days and any expenses are on you of course but they wouldn't have charged any penalty. This only works if you turn up at the airport late, you can't call ahead and say you're going to the flight and expect any sympathy.

So if your going to do something like this better with a US airline (or AC) and not a European one. I know someone who turned up late for an LX flight and was told she had to but a new ticket at full price.