They won't be able to move you on to a later LHR flight to reduce your connection time in JFK, however, if you wanted, they can move you onto an earlier JFK flight connecting to an earlier SFO flight so you arrive at your destination closer to the time originally booked.

Your fare class/ticket type will be irrelevant as you'll be changing the ticket due to a schedule change

Personally as you'll now be arriving 135 minutes later than planned, I'd use that as an excuse to get them to rebook you onto the direct LHR SFO flight which arrives closer to your original arrival time, free of charge

That's unless you're doing the indirect routing for the Tier Points, of course...