Regarding table to retrieve closing balances from:
BalanceLinesPerPeriod: includes company, year, period and general ledger account as dimensions.
BalanceLinesPerPeriodCostAnalysis: includes cost unit and cost center also as dimension.
Regarding incremental approach: both approaches are used in the field. The *Incremental always calculate every row, but bandwidth use can be reduced by using only a vertically filtered selection. Performance after download is not expected to be very different, unless it is a volume over 1 million rows.
Please note that Exact Online has some specific transaction types like 310 for period closing, so make sure the figures align with the web interface.