Four r/t trips LHR-FRA/MUC/ZRH-HKG will bring you LH SEN, yes.
But your math is way off on BAEC. One return LHR-DOH-HKG in Business will give you 560 TP. Then, all you need are 40 TP and 4 BA flights. (The example you mentioned, four r/t LHR-HKG in Business would yield 1120 TP.)
You are right on the LHR-HKG BA TPs. I forgot to multiply by two, my bad. I would however never ever dream of flying LHR-DOH-HKG in business. This is for me nonsense timewise. LHR-HEL-HKG with 440 TP appears to be the more relaxed choice. I am BA Gold and have been for the last 15 or so years, most of my flights are to Australia and as I mentioned BA gives you on this route the strange opportunity to achieve gold status for six releatively cheap F-Class segments on a non-OW airline and a few cheap flights from my homebase on the continent to the UK.
The new LH system is great for people either flying on cheap P-Class returns via the LH hubs (40 QP for return) or people flying taking advantage of the cheap intercontinental P-Class offers. It is to the disadvantage of people flying F/C. Your advice to use TK or other programms forgets that several programms give zero miles/points/kilometers for LH-Group P Class, which offers great fares.
As I mentioned - based on my 30 years of FF experience (and this appears to be my post #10000 on this forum) - you need to make the right choice based on your own schedule and budget and you should chose an airline that most likely still exists in several years (I am personally eg not too sure about A3).