Your first suggestion is correct. Essentially, applicants are considered for MQ's Leaders and Achievers Early Entry Scheme in one of two rounds. In your case, if you do not apply to be considered in the first round but do apply to be considered in the second round, you will still have a chance of receiving an early offer, just as if you had applied in the first round.
You cannot apply in both rounds to maximise your chances. This is because MQ will only assess your application once (i.e. for one round). Subsequently, the outcome will be released on the specified date for each round, regardless of whether your application was successful or unsuccessful. This means that you can only receive one outcome through the Leaders and Achievers Early Entry Scheme and will therefore not be considered for the following round, that is, if you apply in the first round.
I hope this helps!