70 390 Vibration following clutch job

I had the engine balanced as it was intended, using an NOS damper and the original flywheel. I did inspect the balancer this morning, did not see any signs of slippage or damage.

I using the Ford Mustang T5, what is called the World Class version for the V8 engine and was used from 1987 through 1993.  The bell housing is generally called the Multi-bell, used by AMC on their T-4 and T-5  equipped cars.  Multi-bell in that it could be found being used on other 3 speed transmissions during the same time interval.
And you want to be some what careful before making a decision to use something like this in that the gear ratio of 1st is quite low, 4th of course is 1:1 and over drive is exactly that.  Working from memory about .75. I'd have to look up the specifications. 
The point is when doing something like this you want to take into account your rear axle gearing in that if you are planning on keeping the 3.54 OEM final drive, bolting on this transmission with out further though gives you the following:
1st becomes functionally a Granny Gear.
2nd through 4th becomes a wide ratio 3 speed
and 5th becomes an overdrive.
To make this a functional conversion your rear axle gearing becomes about a low 3:XX or a high 2.XX in order to get a workable 5 gear set up.
Those who ignore this generally discover that they were better off not doing it at all.
I am using a 3.15:1 positraction rear axle and the gearing works out quite well for me with road speed in 5th about 32mph/1000 rpm which is quite typical these days for multi-geared OEM cars.
The other thing to keep in mind is that the transmissions are not rated very high in torque.  So if you plan on beating it, death will come early.
I have hear another set up I can assemble one from except in this case I have the same transmission but one as used from a Merkur the German car ford broad in but re-engined it with the Turbo-4 which was also used in T-Birds. The gear ratio's are even wider as 1st and 2nd gearing is even lower than the V8 version. It would have to rebuilt with differnt 1st and 2nd ratio's and when doing that, those values can be selected to be better which both changes the transmission to make it more useful with a short geared rear axle and also improves the torque rating. There are other a couple of other things that can be done to improve the reliability too. But realize again these are now old transmissions and technology has both changed and newer options are open that may not have existed in 1991 or 2 or so when I assembled this. The whole thing is ALMOST a bolt in on an AMC engine and car IF yours already is a standard transmission equipped in the first place and you have a broken T-4 for parts, although that is not absolute, just handy.
I've had no problem with mine and would do it over again in a NY min.
But, I don't beat on it.  Mine was a 4 speed car and  the 4 speed wore out and rather than rebuild it the 5 speed made it much more happier on the South West high speed interstate roads.

It is self evident with out argument that a 4.88 is not a street gear for cruising.  And it can be said a 2 speed power glide makes a good drag racing transmission if you only want to run a quarter a mile at a time.
Multiple gears gives you a low for acceleration and a high for freeway driving and the middle gives you flexible driving. But you can really screw that up by choosing the wrong rear axle gears.  With what you have at the moment the only viable solution would be a gear vendors overdrive which takes care of the cruising gear ratio and leaves low alone.
My Donohue is a nice running 390 built to be a tunable street engine and frankly can be tuned to pass smog and MUST run on 91 octane which is the premium gasoline out of the street corner pump. You have 94 octane out of the street corner pump in Florida.  That says the engine can be different, but it won't run well on 91 octane.
As a street motor mine  is fast and reliable.
The gearing and the transmission lets it be that way.
I've owned it since 1979 and it has seen a quarter mile about 2 miles worth during that time, which is enough for me.
Cheers and have a good day.