Working through recapping my General Electric H76 I am hearing shortwave broadcasts across the AM band. Started to follow the alignment steps and I get a distorted guttural tone when aligning Ifs. Will start over again but can pass modulated rf through set from antenna terminal. Any suggestions? Audio section of the radio works great, was able to input audio from another radio through the phono plug.

Sounds like in the process of recapping you managed to short a shortwave band oscillator coil with the broadcast-band one. Look for solder drips or bare hookup wires around the oscillator coils that might have gotten pushed into contact during the recapping operation, especially in the area of the band selector switch.

The loop antenna is missing in the radio but the 3-wire socket is present. Was there a switch also to go with a long wire instead?

:Sounds like in the process of recapping you managed to short a shortwave band oscillator coil with the broadcast-band one. Look for solder drips or bare hookup wires around the oscillator coils that might have gotten pushed into contact during the recapping operation, especially in the area of the band selector switch.
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I don't have a schematic for this set but there was probably no antenna switch as such. Most likely the (missing) loop antenna had a coupling winding that terminated in external antenna and ground screw terminals on the loop frame. Since the loop antenna is part of a resonant circuit you will need to find or make a replacement for it in order for the set to operate well. Doubt that this is your "shortwave crosstalk" problem but it is certainly a problem in its own right.

Agree with CV. The radio needs a loop antenna, that's why it sounds bad while doing an IF alignment.

the socket has a wire for both the SW and BC antenna coils. Was there a separate loop for shortwave and BC, and black was a common to ground?

:Agree with CV. The radio needs a loop antenna, that's why it sounds bad while doing an IF alignment.
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If there are no screw terminals on the chassis for external antenna/ground connections, you can assume that they are on the missing loop antenna unit. The SW connection would have been a "pass through" that likely connected to the external antenna terminal. A loop antenna would not have been very effective for shortwave reception. A schematic of the set should clear up all ambiguity.

If someone could take a look at the schematic (I would be willing to email it)and give me an idea as to making a loop, number of turns, connections, etc? I would be grateful.

:If there are no screw terminals on the chassis for external antenna/ground connections, you can assume that they are on the missing loop antenna unit. The SW connection would have been a "pass through" that likely connected to the external antenna terminal. A loop antenna would not have been very effective for shortwave reception. A schematic of the set should clear up all ambiguity.
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With a schematic, figuring out the antenna electrical connections is no sweat, but building a replacement loop antenna is another matter. Wire diameter, loop turns, and loop dimensions all factor into making an antenna that can be optimally tuned to your radio, and the schematic is unlikely to have any of this data.

I recommend that you try to locate an example of this set that has the loop antenna intact, then get a detailed description of its construction. That should enable you to build an antenna that approximates the electrical characteristics (and appearance) of the original quite well.

A more labor-intensive and partially experimental approach would be to examine the antenna circuit that has to resonate with the loop over the broadcast band frequency range. Knowing the tuning cap capacity (from the schematic), you can calculate what value of inductor in fractions of Henries would be required to achieve resonance. Armed with this info, you can reverse engineer the missing loop assembly and select the variables (loop size, turns, wire diameter) to achieve the target inductance value.

Once you have a working loop antenna, you can tackle the other problems in the set. If the set won't accept an IF alignment, you have problems with the IF filters. Since you bypass the radio front end totally when aligning the IF filters, if the IF won't peak, the problem cannot be in the antenna or mixer stages. If you can peak the IF filters but can't successfully complete the "front end" alignment, you have a problem in the antenna or oscillator circuits. An oscilloscope or frequency counter can help you sort out the real issue. If you rewound the oscillator coil, that's a good place to look for a problem- if the LO can't track the incoming antenna signal with the proper frequency offset, the IF stages will reject the mixing product.