M1 for travel shortly before UK visa expires / ILR

I am an Australian living in London. I will be eligible for ILR in May (and will apply for it) and my UK visa expires in mid-June.

I am planning to go to the US for training for about a month. The training I am doing will require an M1 visa and I understand I will need to demonstrate that I will return to my "home country" (the UK) at the end of the visa.

Ideally, I would like to travel in April / early May so I can make the most of the UK bank holidays and use up less of my annual leave. (Plus of course if I wait until after I apply for ILR and my application takes a long time, which is common, my trip to the US would be pushed back to very late in the year.)

However, I am concerned that applying for an M1 visa for travel to the US shortly before my UK visa expires may raise issues and my M1 application might be refused. Has anyone been in a similar situation? What was the result of your application, and if successful what evidence did you provide to demonstrate ties to your country of residence?

You'll be travelling on your Australian passport, and even though your UK visa will expire a short time before your return, you're still eligible for a visa on arrival for tourism in the UK as an Aussie. So, as long as you have return flights and you have enough time left on your Australian passport, this shouldn't be an issue.