Brief update. Ended up taking the air filter out as well to get better access. Unfortunately I bought an 8mm ID pump fitting with 8 mm ID clear tubes, but the existing fuel lines are 8mm OD and ~7mm ID. I somehow only noticed that once the were off. All shops are closed to get a 8 to 7 mm reducing piece, so will have to leave it for another weekend probably unfortunately.

EDIT: A reducing piece from 8-7 mm seems a lot harder to find than I thought. Not a chance I'll be able to widen the existing fuel line to 8mm though. Will have to see what the best fix is.

So, i just fitted the new fuel pump, but i am having trouble priming the pump. With the bleed screw undone, it can't seem to build enough pressure to suck up the fuel from the tank. It seems the pump must be installed much lower to push the fuel. Has anyone had similar problems?

I can't seem to figure out exactly where the facet one from the previous photo was installed. I tried in the engine bay, but no luck...

I went with a generic CarBole one.

My facet is mounted under the driver's seat tool storage on my 110, so roughly level with the front floor plates and has no problems pumping.
Have you got it the right way round? Usually an arrow showing direction flow.
Have you fitted it to the flow pipe, that's 10mm OD, return is 8mm OD.
You could try the pump in a bucket of diesel off the vehicle, it might be duff?
Or you are sucking in air badly somewhere downstream, pickup pipe inside the tank might have a hole in it for example.

Today I mounted the fuel pump on the chassis near the rear axle, where a T-junction for the heating system was already installed. I installed the pump in series with the lift pump, as I had read elsewhere online that a few people had done this successfully.

The engine is running, but so far I can't seem to notice much difference. On a "dry start", the engine still needs a few turns before starting and it seems like air might still be getting in the system. Maybe through the fuel line of the heating system, which branches off just before the new electric pump? I'll need to drive a few kilometres to see if the problem persists. Also, hardly any fuel is coming out of the bleed nipple on the diesel filter when only the electric pump is running, which i find odd. I guess the pump is struggling going through the mechanical lift pump and its valve.

I ended up fitting all new T-junctions and adapters through 7.5 mm inner diameter rubber fuel lines. They fit nicely over the existing hard fuel lines which are slightly under 8 mm outer diameter, while fitting on common 8mm t-junctions etc.

Just thought I'd give a brief update. The electric fuel pump did no good. I ended up replacing some piping around the t-junction of the heating system and all the clamps for the piping. Everything has run smoothly since. I'm not sure if that is because the weather is warmer or because I eliminated air in the fuel line by fixing leaky connections. Either way - all good at the moment!