In my opinion something like what happened with the Yak-3/Yak-15 would have been more reasonable, considering that "so many modifications to the various components would be needed that no time would be gained over the Me 262 development", as i've read at the Luft46 site.
This could be done by modifying the 109G or K version, replacing all the frontal section with the engine and fuel tanks with a new nose section, consisting of a single Jumo 004 jet and fuel tanks.
Doing some counts based on comparision with the Yakovlevs 3/15 (and so with no absolute whatsoever scientific value of course
) a single engined jet 109, could have attained a max speed of 873km/h, with an empty weight of 2394kg and a loaded weight of 3307kg. But the combat range would have been of only 462km, that could maybe raised with the use of a pair of droptanks under the wings.
Moreover the single engined solution would have proved more smart, as this variant was intended only as a secondary solution to the Me-262, and so it would have made no sense to take away from the schwalbe production all those engines.
What do you think?