Wow... I'm wondering what mechanics even know these days. I think the first required talent is the dexterity to remove money from a bank account by ringing the cash register.
Here is my wild guess. The engine sat around for lots of years with a crusty intake manifold. The brake mechanic 'gave it hell' and the puff of smoke is when gobs of the caked up intake blew chunks of clinkers into the cylinder, causing one or more valves to stick open. That can also cause the loss of compression and a 'no start' condition.
The rest of the problems are a comedy of errors compoundesd by one mechanic after another.
I don't know how an engine can be an interference (imposing?) engine, have contact with a piston, without damaging a lifter. What is more, the only way the engine block can properly be diagnosed is to remove the cylinder head. No 'and's, if's or but's'.
In my opinion, the timing belt, if it didn't skip, was misaligned. If it jumped time and that happened below 65 mph, the real 'damage' to the piston is you will slighltly dent the valve relief in the piston, usually without serious consequence to the block, but a bent valve. No where do I see how many miles the engine has on it. It could be a really good, low mileage block you'd trade out for a junkyard dog.
All this talk of replacing and engine is very premature without first determining if the piston height has been disturbed. Even then, we have reliably and effectively replaced bent rod sets and reinstalled in engines that went back into service for much less than I hear being proposed. We have rebuilt and installed cylinder heads onto the block with new timing belt for $1600.
More than that, without examining the existing engine, (and by the way, with a lot of man hours to effect the change) with a worse block than what is currently installed? How can you say the pistons even need any work if you haven't examined them? What damage? You need to know what they mean. I'm no doctor, but if I was, I doubt if I'd be able to tell if you had a bad head ache or meningitis over the phone...
The engine doesn't work. It's not going to get any better without looking. The first thing I'd do is pull the cam and look at the lifters... cams in the way. I can't tell, so you can't either... If the lifters are fractured, take the head off. If a piston is damaged, then and only then can you reasonably determine if the block should be replaced.
Here is the real kicker... is it even worth $3500? Probably not. Sometimes, if it comes to that, you have to cut your losses.
Feel free to call, if I can be any additional help.