"There is limited granite along the backside of the sink so reshaping the granite and going with a sink of a different shape is not an option."

Of course there are plenty of options. I've had my metal shop weld faucet decks onto sinks twice now. It isn't cheap, but it's a heck of a lot less than new countertops.

How large is your sink base cabinet, please?

That wide front sink rail may save you too. That can be cut and installed in the rear so an altered sink may not be needed. I've done that several times:

Big swoop in the left bowl and fat front rail just like yours.

Front rail is removed, ripped, and bonded.