Very, very interesting! After staring at the high-res version of the photo for a while, I have convinced myself that the painted designation is F84-CKX. The basic airframe is a very early model F-84 (judging by the pitot on the vertical stabilizer (relocated to the inlet splitter in the F-84E and subsequent) aircraft). The F-84G-type reinforced canopy was retrofitted to surviving early F-84s. So, at this point, I'd take the "F84-C" at face value. As far as the "K" and "X" suffixes are concerned, they are explained by this excerpt from the September 1956 issuance of the "Allowances and Locations of Navy Aircraft".
"Further as to CLASS, aircraft are characterized as to VERSION of basic design by letter designation (as the N in F6F-5N) as follows:
A - Amphibious,
B - Special Armament,
C - Carrier Operating,
D - Drone Control,
E - Special Electronics,
K - Target Drone,
L - Winterized,
M - Guided Missile Carrier,
N - All Weather Operating,
N(A) - All Weather version stripped for day attack,
P - Photographic,
Q - Countermeasures,
R - Transport,
S - Submarine search and attack,
T - Training,
U - Utility,
W - Airborne Early Warning,
Z - Administrative.
The suffix letter "X" is used to denote that a conversion to that model has not been completed. Upon completion of the conversion, the suffix letter "X" is dropped." Of course, this does not explain the F3D-2T2 (oh well!).
Judging from the designation and details in the photo, I'll throw out the following theory...
The subject is a F-84C. The designation reveals that the drone conversion is not complete and that observation is supported by the lack of remote control radio antennas and RF/optical scoring equipment. The mangled designation may indicate the the overhaul, update and painting of the aircraft was performed by either an Air Force Depot or contractor prior to transfer to the Navy. That would make sense because neither the F-84 aircraft nor the J35 engine were in the Navy logistics system in the mid fifties.
The BuNo looks to have been issued around 1955 or 56, judging by the preceding and succeeding serials (F4H-1, A3D and F5D).
My guess is that the Navy determined that there would be a need for a high speed target for test and evaluation of the emerging generation of Sparrow-equipped interceptors (F4H-1, F5D-1, and F8U-3). With no excess Navy jet fighters available the Navy planned to acquire a number of excess Air Force F-84s. The aircraft were allocated and several were transferred to the Navy. At some point, plans changed and F9F-6 aircraft became excess to Fleet and Reserve needs; were available for drone conversion and the F-84 effort was abandoned.
In retrospect, the F9F-6 made a better drone, with swept wing performance and much easier O&M (operations and maintenance) concerns.
Well, that's my reasoning and theory... any thoughts?