I'm normally one of the laid back people on this forum when it comes to restrictions, but for a number of reasons this doesn't seem a good idea. BA will interpret SIN's restrictions quite strictly and anything odd like this is going to raise a red flag, even though I can see it can be argued. In your situation I would take advantage of your Bath Road hotel booking to go across to (e.g.) Collinson, which is in front of the Marriott on Bath Road, to get a 4 hour RT-PCR test.