So, to look at it from the other side. The mechanic didn't touch the bottom end. When you do head gaskets all you see of the bottom end is the tops of the pistons, and if those looked good and there was no complain about other issues you certainly wouldn't go digging for them, especially if you're likely not to get paid for it. Now if he overfilled it with oil on reassembly he assumed some liability, and its possible that what happened could have been his fault. If the OP has him saying that in an email or text or voicemail then that helps, but if its just something he said that no one else heard its the OP's word against the mechanic's and likely that means nothing. So without that the OP has very little other than the old "he should have known" or "he knew", etc., but knowing something and proving it legally are not the same thing.
The hard part legally speaking is going to be proving that overfilling it with oil caused the thrown rod. Civil law cases are decided by the preponderance of the evidence, or in other words simple majority of evidence in the favor of one party or the other. If the OP has 51% of the evidence in his favor and the mechanic has 49% then in some sense the OP wins, but the judge is ultimately going to decide if that 51% entitles him to a new engine or only payment towards it. Of course, what you deem evidence and what the Court deems evidence is subject to the judge's discretion and governing case law. Best case scenario its a crapshoot to sue. Cases have been lost with a lot more evidence. Even if the OP got a judgement its going to be tough if not impossible to get paid. Self employed people have income that is difficult to prove. If he goes off the grid and only takes cash jobs you'll never prove he makes anything. Without a paycheck its going to be impossible to garnish his wages. You could probably try and attach a judgement to any assets of the business, potentially selling his tools, etc., which would bring him pain, but you'd get pennies on the dollar and not come close to making yourself whole after the filing fees, attorney's fees, etc. This is why its always best to sue only as a last resort. Lawsuits are where attorneys get rich and people get screwed. And yep, that's some hard learned first hand experience there.
I'm reminded of a similar situation one of my best friends was in some years back when he did a lot of work on a Mustang for a guy. It had a 351C engine and he wanted it to make 450-500HP. The heads are up to that task (4V heads, huge ports and valves), but it needed a cam, etc. to take advantage of it. Upon pulling the cam with the engine in the car my friend saw the cam bearings were down to the copper. He told the guy he needed to pull the engine and check the bottom end. The guy refused, instead he had my friend install a new set of cam bearings with the engine still in the car. Well, in short order the engine blew up. The guy went nuts, threatening to sue, etc. My friend, who was careful to document everything along the way referred him back to the emails where he had told him the bottom end needed to be checked and he wasn't responsible for it if the engine blew because the guy refused. That changed the guy's demeanor and he then promptly paid my friend to pull the engine, find a new block, and build a stroker with more like 600HP. Knowing the guy had more money than sense my friend promptly put a 5,000RPM chip in the MSD box to keep the idiot from over reving it and having a repeat of the same disaster.