My workaround to this is to have both of the cards synced between QBO and Chase and whenever you pay off the cards, do a manual journal entry to zero out the sub CC and write off the balance against the main CC. For example, if the sub CC is showing a credit balance of $1k after paying off the card and the main CC is showing a debit balance of $1k (because QBO syncs the entire payment to the main CC), then do the following manual journal entry:

Sub CC         DR $1k

Main CC                        CR $1k

I just started doing this so I can't say how it will affect reconciliation, but it seems to fix the numbers in the bank transactions page / trial balance.