Gentlemen,
there is a bit of confussion here

. We are talking about three related but different designs
F-4XBy 1971, the F-4E was not capable to intercep the MiG-25. It was a challenge for Israel AF who faced reccon flights from Egypt.
Israel concluded that the only solution at their hands was the application of Pre-Compressor Cooling technology to increase the GE J79 thurst. The USAF financed General Dynamics to develop a PCC Phantom, resulting in the F-4X project. The most significative modifications from F-4E were the dramatically enlarged and complex intakes, and the water tanks on top of the fuselage (you can see it at attached profile on on dan_inbox's post). Expected performance was Mach 3.2 dash and Mach 2.4 cruise. It would have been a "Foxbat hunter" but that beast was also a threat for the F-15 program. USA Congress was taking several long looks at both the F-14 and F-15 programs during 1971 with the goal of eliminating one of them to save money. F-15A rolled out of McDD's St Louis plant on June 26, 1972. Thus, the F-4X was cancelled and Israel get its MiG-25 interceptor with the F-15A Baaz supplied in 1975.
RF-4XF-4X speed performance so brilliant (even the F-15 could not perform Mach 3.2 dash or Mach 2.4 cruise) that General Dynamics forwarded to the USAF a proposal to develop a reconnaissance version with a new nose section from which radar and cannon would were removed. The nose accommodated the General Dynamics HIAP-1 LOROP camera system. That aircraft was designed to fly a four minute "photo run" cruising at Mach 2.4 while flying at 78.000 feet. The proposal did not progress beyond the mock-up stage because USAF felt it as a threat to the F-15.
The RF-4X, not the F-4X, is the subject of attached profile on on dan_inbox's post.
F-4E(S) ShabloolMcDD F-4E Kurnass deliveries to Israel AF from September 1969 was a serious headache for Egypt's security and President Nasser received help from the USSR in form of an ADF divission which was deployed in early 1970. From that moment, F-4E impunity was lost but also Israeli LOROP operations were neutralized.
A reccon aircraft capable to flight to avoid the SAM was to be sought:
Mirage IV was no longer viable for political reasons
SR-71 and U-2 were not approved for export.
RB-57F with GD HIAC-1 camera was approved for export but, at the end, was denied too.
The GD HIAC-1 fitted on the GD G-139 pod could be carried on the RF-4C centreline station but aircraft performance was downgraded enough to be out of Israeli needs. Israeli AF then suggested the RF-4X which was then on development but the US was reluctant to export such a high performance aircraft. A compromise was adopted in the form of the F-4E(S) for Special.
Project Peace Jack covered the modification of 3 Israeli AF F-4E Kurnass into F-4E(S). The Shablool reccon birds changed its "fighter noses" with the RF-4X "photo nose" an entered service during 1976.
Source: International Air Power Review Volume 19. There is an excellent article from Shlomo Aloni about F-4E(S) Shablool that I strongly recommend. (Well I strongly recommend an International Air Power Review suscription because it's one of the highest quality aviation magazines of the World

)
I also took some bits of info form Aerofax Datagraph 6 "F-15" by Dennis R Jenkins.
Regards,
Antonio