If you convert the periods into date values or a numeric month sequence number, then the calculations are much easier. So during the initial load, load them something like:
(Left(LastReconPeriod,4)*12) + Num(Right(LastReconPeriod,2)) as LastPeriodSequence,
If the current period is defined in a similar way (lets call the value CurrentPeriodSequence), then the colour expression becomes simply:
=If(CurrentPeriodSequence - LastPeriodSequence - If(ReconType = 'Full', 0, 1) = 1, Green(),
If(CurrentPeriodSequence - LastPeriodSequence - If(ReconType = 'Full', 0, 1) = 2, Orange(), Red()))
Here you have a link Canonical Date to a blog above dealing with dates.
If you want customize some cell formats this What is possible with calculated expressions in... | Qlik Community explains some tricks