Engine idle drops and dies after cold cranking?

Only at idle, what does it do if you slightly increase the engine speed while setting? How about this test, Put it in drive and hold the brakes, now turn the blower to high, the headlights to high, wipers on. How does it act now? Trying to see if maybe it's electrical, did you do a fuel pressure test on it?

It wouldn't hurt if it's been that long, however they normally wear and gain clearance and clatter. You said it ran better for a while but now acts up, did you disconnect the battery when you did the other work? I'm wondering if maybe there is a different issue. If you did, unhook it again, let it set a few minutes and reconnect and see if it still acts up? It might still be fuel related but on the other end, the idle is controlled by the throttle body and there is a relearn procedure that it follows and then adjusts over time, however if the throttle body is dirty inside it can cause a low idle as the throttle doesn't compensate properly.
Take a look in the throttle body and see if it has any built up crud, soot. If it does clean it and see if it helps. Book says you need to pull the TB to clean it, but if you have access I generally don't, instead I use a dowel rod wrapped with a towel and spray that with cleaner and scrub out the bore.

https://www.2carpros.com/articles/throttle-actuator-service

Sounds like a plan.

Yep, split hoses can do that as they will cause it to run lean and may cause the other issue you have as well. At idle is when the engine creates the highest vacuum and cracked hoses would cause it to act like it has low fuel pressure and run out of gas. Might want to stick the new hose on and see how it acts. May also want to get a can of carb cleaner and spray some around the other hoses. See if any others are pulling in air. Then if it runs good with no issues you can save some money, unless they are not charging you a ton for the valves.

Please let us know, STEVE W. Is one of our best!