Wub - Thanks for posting the pix, they bring back great memories!
OP - I did the Singapore run quite a few times in the 90s, I used to live in Singers. I always remember the route as effectively being a 45 degree line on the flight map -- as Wub's pictures show.
There were are often variations though. I once remember (flying to London), routing over Iran, flying down the Med and then up from Italy where I got great view of Mount Vesuvius. I presume the jetstream was playing tricks that day. We arrived on time though.
On the way out you may get to experience some tasty CAT over the Bay of Bengal/Andamans, it can be fun!!