For my first FLR(M) almost 2.5 years ago we had to apply no earlier than a month before my fiance visa expired. I held off this time (it expires in early October) to Sept to put it together with that in mind. However it doesn't say that anymore. It just says to apply before it expires. Is that new? Have I waited too late? Do I still have enough time to complete it
It's all about making sure you can qualify for ILR before the second FLR(M) visa expires... so you have to get the timing just right, especially if you are applying in person.
As you are currently on FLR(M) (not a spousal visa), which is valid exactly 30 months, the earliest you can apply for the second FLR(M) in order to qualify for ILR before it expires is 28 days before the expiry date. The latest you can apply is the expiry date.
So, no, you haven't waited too late, in fact, if you had applied any earlier than now, you might not have qualified for ILR before the next FLR(M) expired.
The second FLR(M) should be made valid from the expiry date of the current one, however with in-person appointments, there's always the risk that they will issue it to start from the date of the appointment instead... and if the appointment is too early, the visa may expire too early too (meaning you might need to apply for a 3rd FLR(M) to bridge the gap). So, personally, I would apply as close to the expiry date as possible, while still leaving enough time to get it all sorted before it actually expires.
If your current visa expires in early October 2016, presumably you will reach 5 years for ILR in early April 2019. The earliest you can apply for ILR is 28 days before that date in April 2019... so you need to make sure that your second FLR(M) will still be valid on that date.
Does the first one, "limited leave to remain" refer to or include the FLR(M)?
Yes - that's what limited leave to remain is

.
FLR stands for Further Leave to Remain... and it's limited because it's a temporary visa.
The only reason you may not be eligible to use the service is if you have a complicated application that can't be decided same-day (i.e. refused visas, refused entries, criminal convictions). As long as your application is straightforward, then you can use the premium service with no issues.