Does this plan allow me enough time to navigate Heathrow?

I took advantage of Delta’s D1 Europe fare sale and booked a flight from MSP to LHR but my final destination is Barcelona. My MSP bound return flight leaves LHR at 12:10 on a Wednesday. The earliest flight from Barcelona that day is on British Airways/Iberia and lands at LHR at 8:45 am. I will have to collect a bag and recheck with Delta and will have Sky Priority boarding on my second flight out of LHR.

Three and a half hours seems like a good buffer to make it all happen, but I would love to hear from more seasoned travelers, particularly those familiar with LHR. Does that seem like a reasonable reservation or an invitation for a travel headache?