What EXACTLY is happening that fuel is getting to the fuel injection pump, which we can see is being activated by the cam in the engine but fuel is not coming out of the pump other than a drip or two.
You've certainly done your homework here. Yes, if the injector pump is not putting out, nothing is going to work until that problem is corrected, for whatever the reason is for failure.
Mechanic Two took the pump to his go-to on fuel system issues who took it apart and will rebuild it if possible.
Unfortunately, it sounds as if your pump is not longer on the engine until its rebuild is completed, so the rest of this conversation is only applicable after the pump is reinstalled. I'm gob smacked at Mechanic #1 as he shouldn't even be allowed out on a day pass. #2 Mechanic, I don't know. If there's a certified diesel shop near you, stay away from the amateurs.
The one thing that doesn't sound as if it was done when the pump was attached is to back off the fuel connection, at the injector, on the engine, and look for the high pressure micro spray issued as the starter cranks over. This is a high pressure spray as the result of the injector spring back pressure. I know, sounds goofy if there's no fuel coming out of the pump itself but best to get everything up to pressure (if possible) and see what issues right at the injector. The other big caution here the with all this tubing being disconnected, you may very well have an air lock in the pump. Try opening a fitting on the fuel return to your tank and see what issues. I don't have a manual for your Yanmar YSM12 engine and it may well be different from the recirc system on a Yanmar 2GM20F. Please forward a copy if you have one or you may well be able to find one here on the site. Only requires time to find it.
Sorry, but there's really not a lot of further checking you can do until the pump is back in place.
Please keep in contact with this site when your pump is back and let's solve this problem. I do not think a $10K repower is required IF the pump is properly overhauled.
This is all future work but if your engine still won't run after the rebuild, the above will be worth looking at.