The first assessment is mainly to gauge your eligibility for the HLE since they don't actually disburse the loan and also to inform you of the financing. They will still need a valid HLE during the key collection which is the second assessment. This final assessment is to see how much they can actually loan you, and is not to recheck your eligibility for the HLE.
What happens is that you will get the first HLE with a lesser loan as you said. If there is any top-up required, my advice is to ensure you have that ready in the form of cash/cpf by the key collection time. Reason being if say someone gets retrenched etc, lose job etc right before the 2nd HLE and it is lower than your 1st HLE, on appeal they should give close to the 1st HLE. And if a top-up is required and you can't pay you forfeit the flat, the 5% deposit and the relevant stamp duties and legal fees.
If you actually breach the 10k ceiling during the key collection then you don't really have anything to worry about. When they reassess the HLE you will be able to get a loan that will cover the whole remaining payment. Note that they will makan all your cpf as a lump sum payment and loan you the rest.
