Ok when I had my fip recon on fitment of pump my chain was so slack that the chain sllipped a tooth, on disassembly it expired that the chain hydraulic tensinor had failed resulting in worn away guides now that was a very worn chain and sprockets . Did I have hot start issues no so I'm not convinced . When a pump gets a recon it is stripped cleaned has new seals and it tested with specialise equment not for the like of a main dealer or independent garage thus that is why dealers replace pumps and indeipendent remove and send them off to diesel injection places. Now rebuild is around £600 that will fix seals and have cleaned internals if internals need replacing it is cost effective to renew the whole pump at a cost of around £900. I am led to believe that the problem with hot start is down to a worn pump or the electrical side of pump the top part temp/s or temp
Sensors else where the top cost £300 so you might as well get a new pump this was explained in Lro international with no mention of timing chains
Its not in LRO's interest to advertise a fix that bypasses all its advertisers and costs virtually nothing.
I've folllowed the Hot Start issue for years. There are different causes, some is internal wear in the pump resulting in reduced pump pressure (alledgedly partly curable by adding veg oil to your diesel), some down to internal failure of the timing solenoid (requires a pump rebuild) but the vast majority is down to stretch in the timing chain. I say, the vast majority because component failure is specific to each vehicle whereas wear is the one thing in common to every M51 engine, and virtually every M51 eventually has a hot start issue. QED
You may or may not be aware of the different fuel maps for hot and cold starting for the M51. Inherent in the fuel map is electronic timing control. The ebay 'Hot Start fix' invokes the cold fuel map/timing as well as the glow plugs when starting so is a similar type fix but will only give temporary relief. Once stretch has taken hold your engine is constantly running retarded timing and so will be down on power and use more fuel (a common complaint you'll hear from 'hot-fixers' about a year or so after they fitted the ebay fix.
In my own case my then 115,000 mile P38 went from being a absolute pig to start hot and requiring 2 gos of the glow plugs to start when cold to being a dream starter. It'll now start from cold without glowplugs. Solution, alter the static timing.
Wammers and I and others have had long discussions about this in the past about how and why it works. Those of us with faultmate use a live data reading called 'timing modulation' to set the static timing within parameters. Everyone who has done it has come back a happy camper. Wammers has often pointed out that this is a cure for the symptom not the root cause as we are not doing true static timing which can only be done with a guage. The opinion we've almost collectively formed is that the 'timing modulation' reading is the net timing which takes into account the effect of the timing solenoid as well as static timing.
So feel free to get your pump reconditioned but remember that when it comes back you will be re-timing it anyway so why not try and re-time it first?