In March we may see a new iPhone SE that will have a new form factor resembling the iPhone X, and a larger display, but the physical size similar to the current SE. It will be metal and LCD. It will likely have an A11 Bionic and Face ID. The 6.1 inch may be the iPhone SE Plus. It will also be metal and LCD, and also have the A11. These two phones will be the “budget” phones. The iPhone X2 will be similar to the X, but with enhancements and an A12. There will also be an X2 Plus. So the line up will be two SEs and two X2s. The 8 may be discontinued.
Your March SE is mostly a smaller 8 but with FaceID; that’s not a budget phone, that’s an $800+ phone.
And how is a 6.1” phone an SE anything? It’s larger than the current SE, the 4.7” regular LCD and even the 5.5” Plus. The 5.5” 8 is $799, how would the 6.1” become a budget phone?
The SE is a $349 phone, it occupies the lowest price point in the iPhone line. It’s not going to become a $700-800 phone.
I think the March SE2 gets an A10, TouchID 2, anything else that adds little or no cost, and ideally a price cut to $319-329.
Another possible alternative is the above 4.0” SE2 drops to $299 and an SE2 Plus, based on the 4.7” 6S, becomes the mainstream budget phone at $349-369. Possible changes might be a less expensive display, no 3D Touch, no barometer, etc. Basically, a stripped down 6S, but with a CPU bump to A10.
The SE has sold an estimated 40 million units (many due to lowest price buyers, not smallest iPhone preferrers), while the 6S and 6S Plus have sold a combined 200+ million. There is just not a lot of demand for small phones anymore. I don’t think you’ll ever see an SE-sized, FaceID, X type iPhone.