Do you have any idea how long the new engine ran? Mileage on it? It is tough to start diagnosis without knowing if the person before you messed something up or if the new used engine suffered timing guide failure. If the engine ran normally for a few hundred miles you can exclude improper timing - unless the timing moved, which the compression test may tell you or the timing guides failed. If the new engine was not touched - just swapped moving timing caused by a mechanic is doubtful - moving timing due to timing guide failure is a real possibility.
I just replaced my third engine with an engine (#4 for the vehicle) that had 118k on it. As my prior engine #3 only lasted about 3k, and had new timing guides I installed, I reused them on the new engine #4. I noted when I took off the original guides on #4 that they were about to fail. I could crack pieces with little pressure. I am just telling you this to let you know your "new" engine may have failed - depending on the conditions of the timing guides. I doubt they put in a new engine. Maybe they did the guides when it was out. You need to figure this out to help eliminate problems. If they did the guides - then maybe some timing bolt(s) moved.
I am not sure if your coolant leak is the cause of the problem - but it wouldn't hurt to eliminate it. Can you post a location of the leak? Maybe you can use some of that Silicon tape and seal it up until you can address it correctly. (I love the stuff) Maybe one of the clips isn't seated so it is leaking. Best get rid of all possible problems - I don't know enough to say the engine doesn't have a fail safe.
I would check fuel pressure and do as Mark C suggests - a compression test. Maybe a compression check first. Maybe change the oil and see what it looks like. If you think the oil will be good - drain it into a container you can reuse. Check your oil filter housing bottom for metal sparkle. It wouldn't hurt to drop the lower oil pan after you drain the oil. Look for timing guide pieces. You can do this first or last - but it is easy and mostly just time. You just need to eliminate known weak points. If you do a compression test and it is great, than above can be skipped.
Compression test will tell you if you have a timing issue - maybe your timing guides are shot. A used engine with failing guides is a real possibility.
If you have good compression then the timing should be fine. I would then check your fuel pressure.
To be honest after checking compression and fuel pressure - I would still pull the valve covers, at least Bank 2 and take a look at what you can see of your timing guides. Look for missing pieces, wear, cracks and general condition. Also check to make sure everything is tight on the Vanos and exhaust sprocket and the chains are also not loose. You may have failed guides at which point you need to step back and evaluate the damage.
With a helper you can hold the cams and level them with a ruler, then run a 5-6mm tube through the trigger wheel check screw on the upper timing cover to confirm timing. Crude but for now it will let you start to get to the bottom of the problem.
I will tell you my RR story so you can get a worse case scenario clear picture. I bought my 04 with a bad engine. The prior owner bought it used and at about 50k miles the rear hoses collapsed and ruined the original factory engine #1. He had a shop install engine #2 and ran it until about 112k when the timing guides failed and he drove it until it flat out died and the engine froze. This is how I acquired it. I installed a used motor which was unknown to me junk, engine #3. I replaced the timing guides, vanos ... The engine ran fine, but burned oil at a rate of 1qt every 300-500 miles. On the coldest day of the winter, my wife attempted to start the RR and kept going with the starter until the battery died. In the process, it is my theory, she cylinder washed a number of pistons (the rings were shot anyway most likely due to running low by the original owner). I tried everything you tried - no luck. Finally I drained the oil as it was full of gas from the repeated starting attempts. I noticed metal sparkle in the oil. I dropped the lower oil pan and saw the cylinder walls had gouges. Engine #3 dead. So on to engine #4 - which I just put my almost new parts on and it runs good today.
The moral of my story is that used engines are unknowns - you need to diagnosis issues without spending money with certain known weak points in mind.