The original circuit was perhaps rated for 50-100W output. This was not clearly stated but appears from the design data. At this power level, heat sinks are not required.
The original circuit has only 1.8K connected to C3 and C4. C3 and C4 cannot have 8A RMS in any case.
The modified circuit has been designed for 0.5 kW output and that can certainly give 1kW for a short time (1-2 s)- I have not calculated.
Even for 500W, the C3 and C4 will not have 8A RMS current. (total current 2.4A - that includes losses and with filter capacitors rated well, about 1/2 will come from the capacitors- say 1.2A)
For many applications where you know the load well, simple designs are better and you can get rid of many features.
You will also have to redesign the transformer for higher load (transformer designed for 500W without sufficient headroom may not supply 1kW even for a couple of seconds).
In the original IBM PC AT power supply, they included a separate PFC board but most cheap computer SMPS simply do not bother (they are often rated at 550-650W).
There are several points where improvements can be made in the original circuit but that is a different story altogether.