I have no datapoint for your itinerary.
By policy, BA will not interline bags on two separate tickets, so they would send the bags to HKG. They seem quite inflexible on that policy.

As you mentioned, your hope is that the CX lounge in LHR would be willing to retag your bags to DPS. Policies keep changing and if they are willing to go through the trouble, you would need to have sufficient transit time for them to do it. Not sure they can/want do it on a BA ticket. Otherwise you could ask at CX transfer desk in HKG without entering HK and collecting your bags.