By "give me the results for Run #1", you want the test log to display on screen at that point? Not sure that's possible, the reason being is that, technically, since you are using the project to run the tests twice, the test log is not going to display until the project is done, regardless of how many times you're running it.
The only way I can think of doing it is make sure that under Tools | Options | Engines | Log you set the option to Show Log on Pause and then put a breakpoint on the second Log message.
Now... if you don't need the results immediately after each run, you could set your iterations apart using Test Items. Test items can have a count so that you can execute the same test item multiple times. The test log that results will then have each iteration seperated in the log so that you can see the results seperately. It's not immediate feedback but it will give you seperated results.