I too think that turboprops are no option due to technology and production avaiability issues.
I also tend to think that the XP-58 is no option due to similar reasons. While the plane offers enough space and fuel, it was a developmental airplane, not to get airborne before june 44. The P-38 is avaiable in numbers since 41 and production and assembly lines were working fully by mid 42 latest.
The proposed pure jet engine version is an interesting option. I now am a bit scared about the potential of the P-38 airframewise! Unbelievable but the plane could be kept in frontline service up to the early 50´s with these modifications:
P-38H - mass production started in may 43. As historical.
"P-38I" -mass production could start in nov. 43 (modifications as shown on top of page 1, mix plane. jet engine: I-16 mod 3)
"P-38P" -mass production could start in mid 44 (modifications: I 16 mod 5 engine + 2 Allisons with high speed props, higher set stabilizer and new nose section with fully pressurized cockpit and bubble type canopy = higher crit Mach figure, higher top speed, more range) 8)
"XP-88A" - developmental plane to be ready in late 44. Both Allison engines are removed, the boom structure fully redesigned. The plane is driven either by two I-16 mod 5 (as suggested by Graeme) or by a single I-40. The Modifications are significant enough to justify the new number. Since the plane is both, lighter and aerodynamically cleaner, it will receive substantial advantages and become a true 500 mp/h class fighter. Basically a Vampire, just better.
"XP-88C" - the final version to be made in the late 40´s. Using an improved I-40 engine and swept back, thinner wings, which turn the plane into a true 600 mp/h class fighter.
Neither the Fw-190, the Bf-109, the Spitfire, the Thunderbolt nor the Mustang or any other high performance piston fighter had a comparable potential for further development -if only explored- than the P-38, impressive.