I'm on the five-year SET(M) route. My first FLR(M) was approved on 29 January 2013 and the second on 7 September 2015. I gather the earliest I can apply for ILR is 1 January 2018?
Yes, the earliest you can apply is 28 days before you reach 5 years on FLR(M) visas.
If you have had two FLR(M) visas valid for 30 months each (rather than entering the UK on a 33-month spousal visa), then this will normally be 28 days before your current FLR(M) visa expires.
Is there any concern with travelling outside/re-entering the UK with a residence permit that's expiring in less than six months (as mine is due to expire on 8 March)? I'm planning on travelling to Sweden this week for a few days and the US in mid-December for about a month. My US passport doesn't expire until August 2020.
As long as you're back in the UK with enough time to apply for ILR before your visa expires, you should be fine.
So, the trip to Sweden won't be an issue. The trip to the US might be mean you're returning to the UK pretty close to the expiry date, so you might get questions about the fact that it's expiring soon, but as long as you're preparing to apply for ILR and are aware you need to submit the application before January 29th, it shouldn't be an issue.