The Gun Talk troubleshooting pages should help you solve your problem. I used Step #1 repeatedly on a Mk III 22/45 until it slipped into place.
If you read the other Mk III threads they will eventually have a link to this same troubleshooting page. It is the solution.
The problem is that the hammer needs to be in the uncocked, upright position. But the new magazine safety makes it easy, almost inevitable that the hammer will fall back down into the cocked position.
When assembling you need to use a punch or something to push the hammer upright just before inserting the housing latch assembly. Once you have it stuck you need to follow the instruction on the web page in the precise sequence described.
You will need to (not in actual sequence, see web page for that) remove and re-insert the mag, pull the trigger, point it downward, bang the muzzle on a wood block, turn it upside down and shake it. Basically, you are trying to jar the hammer into the forward/upright position. Then you should be able to finish assembly. I would disassemble and reassemble according to the linked assembly pages (from the troubleshooting page) so you fully understand what is happening and how to avoid this next time.
It is absolutely a probelm with the hammer in the wrong position, and it can fairly easily be jarred into the correct position, even though right now it feels so jammed you can't imagine it coming unstuck short of a cutting torch.
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