Aren't you boarding the train before you enter Russia? Anyway - it seems to me you will have to be at railway station on a specific day, so your flexibility is compromised already.
If you want assistance from me, you will have to offer more detailed information ... over to you.

The assistance I'm requesting here is direction towards a travel agent who can arrange Russian visas without the need of a full itinerary.
Mike, good luck with that approach but I think you could find there will be more traffic and hence a demand for the service in the UK from there and in Europe .
Meanwhile, because the Trans sib is likely the crucial part of your trip, I'd be getting that booked through the appropriate people and using them for any visa requirements and thyen build the rest of your itinerary around that.

Yes mate. All the options are on the table. And I'm considering everything. Thanks for your help.

I fail to fathom how Vietnam gets lumped into the Trans Siberian network. Its not even on the same rail system. And questions on what you actually need to get the Russian visa should be asked on that branch.
Vietnam is part of the pre Sib travel westy as in OP " I'm planning a trip through Vietnam, China, Mongolia and Russia on the Trans Siberian rail network. "
I think you need to interpret the and as a separation but part of his six weeks before getting to the station.

Right. Forget Vietnam and China. Has no bearing on the actual Trans Siberian trip. And as I said, this isn't the right branch fr it except finding an Australian travel agent. But if it was me, I would still contact realrussia.
And while I am at it, you have given incorrect info about Chinese visas.