Sounds like a couple of issues working together perhaps.
The hard starting was originally related to the carb and fuel, but the extra work the starter relay/solenoid was being put through wore it out. And possibly the ignition switch was not sending power to the ignition during cranking and neither was the "I" wire (the Brown one mentioned already) from the over-worked starter relay.

The backfire pretty much confirms you were still getting fuel pumping into the engine during cranking, but with no spark it built up in the exhaust until you let off the key and then the spark and burning combustion gasses ignited what was in the exhaust. Resulting in the big-bang theory.

Good catch, but just one issue added to the others.

Maybe it's not dumping anymore, but it's still putting gas into the engine while cranking.

Now THAT's the kickier! Not sure what's going on there yet.

You still have the old one? You can test it with an ohm-meter and then compare to the new one. It's possible that the new switch is defective. Unfortunately new parts have us chasing our tails more often than we'd like because we assume they're good.

That's not enough first of all. Yes, it's only slightly lower than it should be, but you really should have between 7v and 9v if I'm not mistaken. The others will know based on ohm rating of your particular year's resistor wire, but pretty sure 5.v is too low and points to either a failing resistor wire, or just as likely some corrosion on connectors and switches and such.

Should not be related, but shows that you do have an old electrical system. I would replace the main headlight switch, add relays to your headlight wiring, but check for voltage drops in the wiring first anyway.
The headlight switch has a built-in circuit breaker that is shutting off due to too much load. This comes from either the circuit breaker just getting old, or the wires having too much resistance, or something related to that. Are they updated halogen headlights by any chance? If so that may have put the old switch and wiring over the edge, even though they're just "stock replacement" rated parts. Newer ones still seem to create conditions where the switch dies a little after.
Been there, had that at the worst possible time.

Does your '76 have a Dura Spark ignition, or points? Or perhaps some other conversion?
You will need to test a few things to see what's going on. You've already found low voltage at the coil both with the key ON and in START, but dig a little deeper.
Test for voltage at the coil positive while the points are open, or the ignition trigger is not closing the circuit. This should net you almost battery voltage at the coil. Check the battery first so you can see how much if any you are losing. Do this with the setup cold, where the key has been OFF for awhile.
With no load on it, even the resistor wire will flow a full 12v sometimes.

You can also check the resistance of the wire, to be sure it's within spec.
If Dura Spark, you need to make sure you have 12v to the power wire at the module. And have power to the START wire at the module too.
You can start by testing the Green w/red and the Red w/green wires on the back of the ignition switch to make sure they're hot in both ON and START. If not, then your new ignition switch is defective.
If the switch tests good, then test the wires out at the coil and module.

Also if Dura Spark, might as well test the distributor trigger/pickup by testing resistance between the Orange and Purple wires. Should see between 400 and 800 ohms. Anything near the limits, or outside of them, needs a replacement unit.
This last will likely not have anything to do with your problem, but might as well check while you're at it.

Let us know what type of setup you have though, and maybe something else will come up.

Paul

 

I have the duraspark ignition.
It has about 12.3V at the box itself

Between the Orange and purple wires on the distributor, it was at 629 ohms.

I didn't have time to test the rest of the stuff yet but I will pretty soon

 

That's a great reading at the box. Shows that the wiring between the battery and switch, and then switch to module is in really good shape.
An appropriate test for your situation though would be to also test that same wire with the key in START. If you show 12.3 when in the ON position, but zero (or something near that) when in START, you've found your problem.
Or at least one of them!

Paul

 

So I tested the voltage going to the ignition box while cranking the engine over,
and it went from 12.3 V (Key in the ON position) to 1.15 V (Key in the START position).
Yikes!
What would cause this? Old wiring?

 

My first thought is same as before, that the new ignition switch is bad right out of the box. Somewhat common unfortunately.
Aside from that though, I'm still thinking about what else might cause it.

Just to be sure though, what connector and wire color were you measuring the 12v in ON at (a very good reading I'd say, showing that at least that one wire is in great shape) and was that the same contact that went to 1.15v in START? Or was that low reading from the other connector?
Obviously it's too low no matter which contact the reading is taken at, but if it's at the normal power-in connector, that's why your engine won't fire during cranking. With no power to the module during START, there will be no spark from the coil.

The more I think about it, because the wire tests good to my way of thinking (from seeing 12.3v when ON), it has to be the ignition switch losing it's connection in START.
We know the START function of the switch works with regard to the Red w/blue "S" wire to the starter relay, because the starter cranks. But the Green w/red wire is a separate contact and appears to be disconnecting when in START.

Test the old switch with an OHM-meter to see what you get on the different tabs, then compare it to the new one.

Paul

 

 

Thanks for that!

 

This is the connector I used to test the voltage going to the Ignition Module. I also attached a video of me cranking the engine over and showing voltage at the connector going to the box.
[NOTE] Immediately after the video was taken, I plugged the connector in and the engine started with the key in the START position with no issue.
Unfortunately I no longer has the old ignition switch to test so i'm just going to get a new one. (They are only $13-$25). But this time I am going for the more expensive one.