A good strategy to support this deck

You didn't say where you are located, but i figured in a cold area like me in Maine. First of all, 12 inch joist spacing a a waste of time and money. 16 inches will be fine especially if you plan to use 5/4 decking of any type. If you are in a non ground freeze area, just use simple blocking to support the additional 4 foot off the concrete. Assuming you are in the frozen north, consider using 3 foot porch posts. they are pre-poured concrete pyramids with a threaded insert dead center on the top. Often easier that sonotubes and mixing concrete. If your existing slab is not underfooted with a frost wall, and has not heaved or cracked over the years, then most likely a simple 8 inch concrete block in the ground the same depth or slightly deeper than the slab will probably do just fine. Remember you are only supporting 2 foot of deck (2 ft supported by slab and 2 ft supported my new foundation) and the decking itself will be spanning 8 to 12 feet onto the existing slab. Over kill is fine, always safe, but not always a good use of time and money. Also if you new deck is 12 inches off the ground, please consider some safe egress steps and side barriers. The rise of the step should not exceed 8 1/2 inches. A 12 inch step down can be a hazard, especially at night and for younger and older folks. Check your local code or the new IRC guide lines.

This is one of the reasons free standing decks are not a good alternative to a deck that has been engineered, permitted and structurally connected to the house.

Using the house to fix what is, essentially, a foundation problem with the deck will not necessarily go well. It is not likely that all parts of the deck moved away from the house equally (structures don't usually "slide" around.) It is more likely one side has dropped opening a gap on the house side. This is common, and can usually be fixed by jacking the outside edge back to its original position.

Worse case you will need dismantle and rebuild the deck, sitting it on proper foundations constructed below the front line, and anchoring it to the home's rim joint.