I'm not sure if it is even a help but you might consider the tape used to mask off things like gold fingers. If your volume is enough I'm sure the tape mfg or a value added supplier can precut "dots".
I was also wondering if putting tape over the hole in the sensor and heating the assembly might risk over pressuring the pressure portion of the sensor.
If you haven't already, I would go back to DigiKey. If for no other reason than so others don't have to suffer a similar issue.
I actually had a phonecall with my PCBA and it turns-out that he used vapor-phase oven to "cook" this proto batch.
As it's stated in the HSMI document not to employ vapor-phase oven, I guess I have my culprit... Note that one (out of 20) of my BME680 apparently survived the process and is working normally.
So I'll make a new batch with proper reflow and see how it goes.
Just a last update on this thread: I got a new batch of my BME680 daughtercard (no vapor-phase this time), and it looks good.
Thanks again for your support.