A quick fix for the OP (other than a capacitor) would be to use a lab power supply to subtract the offset. Set the output of the power supply to the offset voltage (7.5V), connect (V-) to the GND of the DUT and use BM689S to measure the AC voltage between the measuring point and (V+) on the power supply (as opposed to GND or V-).
This idea also crossed my mind - but it does introduce some other concerns.
Not having any practical expertise in this area, here are my observations:
The PSU would, obviously, be floating, reasonably stable and have (ideally) zero ripple. It wouldn't need to be precise - just close enough to the 7.5V offset that it brings the input to the DMM's ADC within range.
How practical it would be is another question. Having extra leads floating around increase both mechanical and EMI risks. There is then the time taken to set up such a rig - with the risk of errors doing so - plus the expense of purchasing another piece of gear. Also, is there somewhere you could place such an item in the production floor environment? Not to mention the fact that, if you are going to have some calibration history requirements, this PSU would need to be certified (as I understand it).
This sounds to me like a classic case of "Buy once, cry once". As others have said I, too, would recommend the "bite the bullet" direction. The pain will only exist at the initial point of expenditure - but if you go down the "cheaper" path, it will flare up repeatedly - costing you time, money and reputation - until you get to the point of wanting to rip your hair out. In desperation, you eventually cave and fork out the funds to do it right then a month later you marvel at how smoothly things are running and kick yourself for not having done this in the first place.
This applies to ANY situation: Get the right tool for the job. I daresay we ALL have had experience here - whether working on electronics, your car or any other task.