The 707-120/720 upgrade was not done by all operators, but the large (in fact huge for the time) fleets of both which American Airlines had built up very early on in the jet age were fully done. Some of their older turbojets were only months old when done and American changed over at the end of 1960 in mid-delivery of their fleet as soon as able to do so. I believe the only operators to actually do the upgrade were Pan Am, American, Qantas, and a few USAF VIP aircraft.
I did understand that once the orders for re-engining suddenly started Boeing realised their mistake, and the 707-320B upgrade from the 707-320, in hand at the time, was deliberately re-engineered, with spar and structure mods etc, on command from the marketing team, so simple engine upgrades would not be possible on the same certificate, and the operators would have to buy complete new aircraft instead. As this was actually what happened, there seems some credence to this. Although the 707-320B upgrade was not as marked for power, fuel consumption reduction, so greater range, was significant, and also smoke and noise reduction, which the early 707s had caused to become a major political issue.
Were they wholly new engines or just reworked with a fan on the front ?
Regarding converting the RR Conway aircraft to P&W power, I believe no 707s were done but one or two DC8s were. It proved not cost-effective.