Unfortunately this is quite a common situation in practice, which highlights the need to follow the procedures in the contract to avoid such 'problems' from arising.
From what you have said, if the PM's assessment has been notified to the Contractor, including providing details of the assessment, then the compensation event has already been implemented.
The Contractor's re-submitted quotation (referred to as CE in point 5) doesn't relate to anything because there is no 'open requirement' on which to link the quotation to, so the PM is under no obligation to do anything with it.
If the Contractor was 'too busy' at the time to submit a quotation, then there was an opportunity to extend the 'action time' by agreement.
The next step should be adjudication.
With reference to 'forecast', this should not be a difficult issue, especially if there are details provided with the assessment, including details of how the forecast was made. Unfortunately most of the time a forecast is based upon a vague, subjective opinion, which naturally leads to disagreement. A forecast should (and can) be calculated in a logical and methodical manner, using relevant cost data and information and by sensibly projecting this forward to a defined point in time, taking account of any specific issues which may influence the outcome, ie: access restrictions, working hours, Contractor's weather risk, co-ordination with Others etc. No amount of 'experience' or 'expertise' can produce an accurate forecast without sensibly considering this process. The 'experience' part is essentially a sense check on the outcome, rather than just churning out numbers.
Take a weather forecast, for instance. It is based on a simulation of current trends and projected forwards in time, taking account of any particular localised conditions. It is not always correct but usually not that far out, unless it is projected a long way forward in time where small variables may cause a different outcome.
It doesn't matter if a forecast differs from actual, it usually will as it is subject to 'variables' and is not an exact process, although more important is that it has been assessed correctly and properly.