No start

Look at the crankshaft layout and you will see that you can move it to 90 degrees off top dead center in either direction and the pistons will be lined up halfway down the bores. That will allow you to move the cams without hitting the valves anywhere. Then you can set the cams in position and get the crank into place after the cams. DO NOT TRY TO FORCE IT.

I would pull the cover off so you can get to the chains and then make sure that everything is engaged. If you have enough slack that the chains can move I think you will probably be needing more than new timing chains. From that description it sounds like the tensioner failed. That would have let the crank turn without the cams moving. I would probably just pull the chain and pull the head and be sure of what you have before going any farther. A slightly bent valve would let you turn the engine over but still be junk.

What you need to do is determine that cylinder 1 is at TDC or coming up on TDC. Then leave the crankshaft 90 degrees away from that position, with number one ready to come up on TDC. Then rotate the cams into position. Now GENTLY bring number one up to set the crank to TDC. You cannot just rotate the cams with the pistons in the way.

Now you can remove the chain and reinstall it so the marks line up. If you just try to rotate the parts with the chain on you will just do more damage.
As it is I think you have a dead engine if that tensioner failed and that engine turned over even one time with the chain jumping. That is one of it's known failure modes. Valves get out of time, piston comes up in the bore and hits the valves just like hitting a nail.

Nope. They will machine the head and install new valves as needed but you will still need to do the assembly.

The way I would proceed if it was my engine: First I would remove both cams from the head after marking all the parts and taking a few pictures. Then I would do a leak down test of each cylinder to verify that it does have some bent valves. (it would be incredible luck for there to be no damage, about like walking out the door and finding a stack of gold with a sign with your name on it)
The leak down test shows that there is leakage past valves in two cylinders. Next step would be to drain the coolant and pull the head off. Then look for the telltale marks of the valves hitting the pistons. I have seen them just scuff the surface and I have seen them go right through the piston tops and everything in between. IF it's just minor scuffs and it didn't hurt the lower end I would then have the head rebuilt. If it is more severe I would either replace the engine with a used one or get a remanufactured engine.

It all depends on what the damage is and how bad. But it would start with the leakdown test. With the cams out it would be easier. Just connect a good air supply of about 50 psi. to the spark plug hole, gently apply air and let the piston go to the bottom of the bore and listen at the intake and exhaust for air. Then turn off the air and rotate the crank to bring that piston to the top and lock it there and test again.

https://www.youtube.com/watch?v=N6UDPd7yIjE

The marks would be the ones left from the valves hitting the pistons.

The cams should be out when you put the head back on. Then you just bring number one to TDC. Make sure the chain is correct on the crank and the idler. Then you install one cam. Line up the plated chain links with the correct marks, install the other cam and line up those marks and release the tensioner.

Where the cams are NOW won't matter one bit as they have to be removed from the head before they can work on it anyway. So just strip it down, get the head finished and put it back together. You will want to replace ALL the chains and guides as well as checking over the rest of the engine for problems.