After watching this
https://www.youtube.com/watch?v=kqFMGEuMP1o I came to realize how poorly executed the trans-Siberian railway was. From poor quality steel rails, overly spaced and green lumber for ties, a disaster of a lake ferry, etc, etc. it's a true demonstration of engineering and national incompetence and over-reach. The video reports that 1/3 of the national budget went to building the railway, which upon completion had a top speed of 15 mph, while trains in the USA at this time were setting records of over 100 mph and regularly running at 50-60 mph or more.
So, without ASB, how can we build a better trans-Siberian railway? Starting in 1891 per history, but hopefully ending before OTL 1916. The TransCanada railway, from Bonfield, Ontario to the Pacific took from 1881 to 1885. This railway is significantly shorter than the transSiberian, but it goes over similar terrain (mountains, swamps, rivers, etc.).
Thus, the best suggestion, IMO, is to outsource the trans-Siberian railway to Canadian Pacific. However, the reason the Russian railway was built so shoddily was lack of funds, industrial capability and skills. Canadian Pacific can provide the skills, but funds and the ability to supply quality steel and materials in sufficient quantities is outside CP's control. Of course the biggest barrier to CP's help is the view of Russia within the British Empire, as this is the height of the Great Game.
To pull this off Russia needs: money, engineering expertise, a degree of political/economic stability, control over corruption and lastly excellent project management. Now it's starting to look like ASB territory, even for today's Russia.