01 mitsubishi montero magical start

This sounds like exactly the same problem I'm having with my '99 Galant (and if your Montero/Shogun/Pajero as it is known is .petrol you will have the same ignition system). It never starts first time from cold even with the key. I've tested and wired up all the ignition leads from the switch, 1 x acc, 2 x ign (one live while cranking) 1 x starter, played with crank time, played with tach (pumped idle speed up to 1000rpm) all to no avail. The only clue is I pulled the antenna from the ign switch and buried my only chipped key in it, 2 x immobilisers on the UK Thatcham alarm.  I use the unchiped key in the ignition.

Do Fortin or Trilogix market a KEYLESS transponder by-pass that I could use instead of a 556UW?

If it cranks and wouldn't get up & run, usually one of the ignitions is not powered up. It happened to me once, could be related to the type of starter I used. I reconnected the acc1 to ign2 and the problem was solved. If you powered up the blue/red as an accy, try power it up as ign 2.

You're testing right...but the 556U, in addition to needing wired correctly, also needs to have its antenna ring positioned correctly around the key cylinder.  20 seconds cranking without startup means the car's immobilizer isn't seeing a valid key and it's disabling fuel.

If the ring's off from the ideal position, then what will happen is that the bypass will work fine when the key in it is at ambient temperature. When the key gets cold, it doesn't send a strong enough signal to reach the factory ring around the ignition switch, the car think's it's being started without a valid key, and it cuts off fuel.

Don't laugh it this solution - I've done it before and it's ended hours of frustration.  Put the 556U, with the key in it, in your freezer overnight. Take it out when you're ready to install it...reconnect it and then remount the antenna ring in a position that will work with your frozen bypass box. That should solve your problem.