The Romanians had their IAR-95 supersonic fighter project, that considered the Spey. They also set up to licence produce the Spey, as part of the BAC 111 programme.
They were happy to supply South Africa with Aerospatiale Puma airframes made under licence.
But I don't think the Spey was seriously considered for the Carver.
The engines that seem to have been most seriously looked at were an indigenous engine, the SMR, or the SNECMA M53 and M88.
The M88 was to be used on the Novi Avion project by Yugoslavia, and would be purchased and diverted through them.
I have read that the Yugoslavians wanted a very high price for them...too high in fact.
The M53 would have been bought through an intermediary, likely Israel. They were offering it as part of the Nammer after all. Taiwan also ended up operating the M53 powered Mirage 2000, and there was a well established trade channel and military links between Taiwan and South Africa.
The local engine was likely an upgraded ATAR, 10% more thrust, lighter, improved components, and more carefree throttle movement. This would have been followed by a local engine.
This would have been the most expensive option. It was doable, but would have required treasure (a lot!) and sweat.
The SMR was an easy option available later, but the Air Force was unhappy with the overhaul and maintenance issues. A major sticking point was overhauling locally. The Russians were resistant.
It was considered imperative to be independent.
In a nutshell, from what I have gathered:
The M53 or M88 were sought after as the most logical, efficient, cheapest, quickest solution.
A local engine, via an upgraded ATAR as an initial step. A very expensive, longer term solution, but work had already started on technology programmes to this end.
The SMR was a late option, but there was serious resistance due to maintenance/ independent overhaul stuff.
So in other words, the usual two-tiered approach South Africa took to weapons programmes. High and low end, local and foreign options.
This last point brings us back to the Lavi, and why it would not be simply built in South Africa.
The entire point of Carver was an independent fighter.
It had to be a local design, and be supportable locally, and developed through future variants locally.
This was as a result of various programmes being cancelled previously through pressure, such as the corvette programme, amongst others.
It is why money was spent ramping up design and R&D facilities in South Africa, such as the extensive wind tunnels, and computerised design facilities.
And why the Carver went ahead instead of just co-developing Lavi with Israel.
And why there were never any serious reports, apart from maybe early on in the Lavi programme, of co-operation between South Africa and Israel on the Lavi, regarding funding and design.
As said, costs could have been shared, via sub systems (radar/avionics/EW/ weapons/ancillaries such as ejection seats, tyres, transparencies..the list is endless).
I am sure South Africa would have loved to get the PW1120, but even IF (a big if) the US turned a blind eye, once Lavi was cancelled, and Bet-Shemesh were no longer going to licence build it, that was that.