Be careful. There are several ways Congress can intervene here, and some of them are bad - in fact, most of them are bad.
1) They could pass a law that every state must recognize every other state's permits. This is probably unconstitutional, since most permits are issued under a state's police power, and there is no general Federal police power.
2) They could create a Federal CCW permit, good in all 50 states and DC. Lawmaking being what it is, this would be as hard to get as the hardest local permits, like NYC or DC.
3) They could make Federal funding for police departments contingent on reciprocity with the 49 other states. This would be the fastest, simplest, and likely most effective method, although I hate this kind of Big Daddy coercion in general.
What they should do immediately is pass DC reciprocity. I was caught up in a flash mob at the National Zoo in 2011, with seven small children, and a guy was stabbed 20 feet away. I wrote immediately upon returning home to FORMER Senator Kelly Ayotte (yay!) asking for DC reciprocity, she wrote back some stupid letter about her budget strategy.
I would imagine that Trump has in mind a system like the one for commercial drivers. Since this is a clearly Constitutional issue it is a clearly Federal matter.
I agree that it is possible that Congress will if not watched very carefully, screw it up.
Your #3 would not stand. Actions like that are viewed as punitive and the USSC has thrown out similarly worded laws. See the USSC case Independent Business v Sibelius. The only way to make your #3 Constitutional would be against future funds. But Congress could not threaten to withhold funds already allocated under an existing framework by changing the terms after the fact. But they could tie it to future funding, similar to the way they coerced the states to adopt Common Core.