In listening here to this discussion, it sounds most likely that you have an engine assembled out of individual parts "uncoordinated" by the builder and that reeks of an un-knowledgeable builder.
Internally balanced engine rotating assemblies often use Mallory metal to achieve that objective. It doesn't happen often but on occasion those slugs of Mallory come loose. It shouldn't be but this is one of the reasons that who is in charge of the project does need to have enough hands on knowledge to recognize an issue on the spot.
An average enthusiast with a fat wallet is not necessarily the person that should be in charge of the project.
Dieseling after shut down is most likely an indication of wrong initial ignition timing as well as no power response.
The Holley mechanical secondary carburetors, i.e., "double-pumpers" are set with race car idling fuel mixtures to, in Holley's words, keep the header scavenging from leaning the mixture immediately off of idle.
That generally can be EASILY fixed by adjusting the idle air restriction. That carb that you have should have removable "air jets". That's where one would start and it will be helpful to have an air/fuel gauge installed with an oxygen sensor in the exhaust.
In MY experience, ALL Holley "double-pumpers" out of the box will have your eyes smarting at idle. That is to be expected of them. That can be corrected without NASA knowledge and equipment.
The "vibration" could be caused by several factors and may be a combination of different issues occurring simultaneously.
The first thing that can cause this is the ignition timing set wrong.
The second thing, which is less likely but possible, is that you have an external balancer and flywheel installed with an internally balanced rotating assembly.
The other thing on a Pantera is that the half shafts need to be sequenced with the differential. You would have to be experienced specifically with Panteras to initially know that and how to do that.
I would suspect that there is no serious damage done to your car at this point. All of these issues are very correctable but will take some time to do by both a competent engine shop and a Pantera expert.
The largest shame here is that the folks you trusted and paid to do this, at least were unsuccessful and likely COMPLETELY ignorant buffoons?
I suspect that you are going to wind up with the right shop eventually and some here can help with that depending on where you are in the country? I can think of a few already and a few are right here on this Forum.
You are going to be the one who determines if you paid for this already with the current "shop" or if this is beyond what they offered? Keep a tab on what this all costs to get right and then consult with a lawyer that has experience with these types of situations. You don't need a legal buffoon involved to complicate things more.
Although it seems like a mountain right now in front of you, you are mostly frustrated and you just need time to dial this car in.
This is all you did to the car right? You didn't touch the suspension, brakes and tires too, did you?
I'm thinking that your "project" created what I would describe as a "brand new virgin race car" much like the initial GT40's were when they were delivered to the first "customers" like Shelby American in LA. They got the first three.
Wanna' discuss what was wrong with them at that point? How about...everything?
It took about three YEARS for two race shops, Holman-Moody AND Shelby American to make those cars competitive. How much time you got?