I also don't like the idea of a button. It is a bandaid for the problem that currently the matchmaker doesn't do a good job.
Your example match of 700 + 1200 vs. 1300+ 1300 has a whopping 700 rating disparity. For established players this shouldn't match, because the chance for the first team to win this is extremely small.
At the moment it does match eventually, because there is a bug in the current server version that rates extremely badly balanced games better than it should. If you want to play this anyway you could ask in aeolus who is queued up and if they want to play a custom instead, but this doesn't warrant an extra ui element.
To give you all a better understanding of how the algorithm works, I prepared some graphs for you. I created a script that passes artificial data to the matching algorithm and plots the results. In the bottom right you can see the rating distribution used for that run. Newbies are people with at most 10 games played in that rating. The distribution is based on real data based on global. Newbies get extra bonuses to match faster. This is especially important, because they can drop to extremely low ratings if they lose their first games and they would have the same difficulty to get matched like top players. We don't want them to get stuck, so we need to help them a little to get games. "search" in the diagram refers to a queued up party, that can contain multiple players. In the top right you can see the wait time of each search based on their average rating.
The graph in the top left shows some metrics about the created games. The games where sorted beforehand, so the game number doesn't correlate to when the game got created. Rating disparity is the difference in total rating between the two teams. Rating deviation is the standard deviation of the ratings of all the participating players in the game. Skill difference is the rating difference between the lowest and highest rated players in the game. It is roughly 2,5 to 3 times the standard deviation. This is just mathematics. You can ignore the rating deviation line and instead focus on the rating disparity and skill difference, because these are the "hands on" game metrics. Finally the graph in the lower left depicts the wait time again. This time sorted by wait time. Honestly the most interesting part are the averages and means written in the top right corner of the plot.
All plots have fixed y ranges (except the rating distribution). I did this, so it is easier to spot differences. This means however that some very high values are cut off. I consider these outliers, so it doesn't matter too much, just keep it in mind. I still have the maximum values in my spreadsheet.
This should be enough introduction, let's start with the bucket team matchmaker. This one was used until the server update 10 days ago.
The currently running configuration of the new matchmaking algorithm looks like this:
As you can see it improved the overall game quality and equalized the wait time a bit. It still suffers from extremely bad games, just like the bucket team matchmaker. The reduced wait time outliers is what you experience as getting very bad games when you are high rated or are queueing during quiet hours. This is mainly because of the mentioned bug, but we can still get some more performance by tuning the parameters.
This is what I came up with, that will be available with the next server update:
As you can see the lines in the top left don't go off the charts anymore, so we got rid of the horrible games. The general skill difference also improved a bit. The top players are back to being in queue forever if no suitable match can be found. The careful use of bonuses makes sure that we match more aggresively on the lower rated end. By the way, this is why you see these spikes at the end of the curves. They are the newbie matches being more lenient with balance.
Because the algorithm is configurable we will even be able to see some of these improvements before the next server update.
I hope I could answer some of your questions. I know that I covered a lot of stuff and I just glanced over some of some of the details to keep the post readable, so if you have any follow up questions, don't hestiate to ask.