Dr.Jass
Pastor of Muppets
On the axle shafts:
The adjuster needs to be backed off completely. If it's not, you will never get it together. The axles should never be pulled in by the studs (in fact, pulling anything together with threads is a terrible idea unless you're installing a wheel stud). If they won't go in, either they're the wrong shafts (not really possible in this situation), the adjuster is not backed off enough, or the differential splines are not aligned.
Inside the differential, assuming you have a cone-type or early clutch-type Sure Grip, the side gears are splined, as are the cone clutches (cone type) and clutch carriers (clutch type). That means the axle shaft has to go into a two-piece spline. The splines in the cones (or clutch carriers) may not be perfectly aligned with the side gears, so the axles start to go through the first spline but hit the other. Try rotating the wheel flange on the axle back and forth while you're inserting it. Put some effort into it; you've got spring pressure to overcome. That should do it.
You can see what I'm talking about in the following FSM images. The side-gear splines are tinted blue, while the cone clutch or clutch carrier ("retainer") splines are in purple.
The first is a cutaway diagram of the cone-type Sure Grip used mid-1969 through the end of the RWD era, which is what's most likely in your axle:

Here's the mid-1968 and older clutch-type Sure Grip (a.k.a. Dana Powr-Lok) with the case half off and the clutch carrier in the disembodied hand (even Thing from The Addams Family had a day job):

What's evident while looking at either photos is there is no factory provision to keep the inner and outer splines in alignment. That's the axle shaft's job. If they misalign, installing the axle shafts ain't happening until you get them aligned. Rotating the wheel flange back and forth as you push the axle into place should do it.
Assuming that passenger-side wheel-bearing adjuster's backed off, that is.
There is a rare, mid-'68 to mid-'69 clutch-type with a 1-piece axle spline, where the back of the side gears actually carries the clutch plates. The "retainer" or "clutch carrier" literally floats on the side gear and acts only to apply the clutches. I've only ever seen four of those, and I bought all of them. I sold one to Stretch, one on eBay, and still have the other two. It's absolutely the best factory performance differential.
The kickdown rod definitely looks like it's the right shape, but is clearly a 2-barrel rod. I don't envy trying to find the right one, since they're not stamped with numbers to my knowledge and you almost have to trust the seller or get one with measurements to know it's going to work. The Lokar cables apparently do work, although their construction and quality has not been described in kind words by those I've heard speak thereof, especially considering the price.
Bouchillon Performance offers them too, I believe, and those are likely even sillier in terms of price. Dealing with Bouchillon on the phone is not pleasant, unless rude and condescending are your type of guys. I bought one part from them online for which they were the only source (and wildly overpriced at that), and that was enough for me. I'll never deal with them again unless I simply can't avoid it.
The adjuster needs to be backed off completely. If it's not, you will never get it together. The axles should never be pulled in by the studs (in fact, pulling anything together with threads is a terrible idea unless you're installing a wheel stud). If they won't go in, either they're the wrong shafts (not really possible in this situation), the adjuster is not backed off enough, or the differential splines are not aligned.
Inside the differential, assuming you have a cone-type or early clutch-type Sure Grip, the side gears are splined, as are the cone clutches (cone type) and clutch carriers (clutch type). That means the axle shaft has to go into a two-piece spline. The splines in the cones (or clutch carriers) may not be perfectly aligned with the side gears, so the axles start to go through the first spline but hit the other. Try rotating the wheel flange on the axle back and forth while you're inserting it. Put some effort into it; you've got spring pressure to overcome. That should do it.
You can see what I'm talking about in the following FSM images. The side-gear splines are tinted blue, while the cone clutch or clutch carrier ("retainer") splines are in purple.
The first is a cutaway diagram of the cone-type Sure Grip used mid-1969 through the end of the RWD era, which is what's most likely in your axle:

Here's the mid-1968 and older clutch-type Sure Grip (a.k.a. Dana Powr-Lok) with the case half off and the clutch carrier in the disembodied hand (even Thing from The Addams Family had a day job):

What's evident while looking at either photos is there is no factory provision to keep the inner and outer splines in alignment. That's the axle shaft's job. If they misalign, installing the axle shafts ain't happening until you get them aligned. Rotating the wheel flange back and forth as you push the axle into place should do it.
Assuming that passenger-side wheel-bearing adjuster's backed off, that is.
There is a rare, mid-'68 to mid-'69 clutch-type with a 1-piece axle spline, where the back of the side gears actually carries the clutch plates. The "retainer" or "clutch carrier" literally floats on the side gear and acts only to apply the clutches. I've only ever seen four of those, and I bought all of them. I sold one to Stretch, one on eBay, and still have the other two. It's absolutely the best factory performance differential.
The kickdown rod definitely looks like it's the right shape, but is clearly a 2-barrel rod. I don't envy trying to find the right one, since they're not stamped with numbers to my knowledge and you almost have to trust the seller or get one with measurements to know it's going to work. The Lokar cables apparently do work, although their construction and quality has not been described in kind words by those I've heard speak thereof, especially considering the price.
Bouchillon Performance offers them too, I believe, and those are likely even sillier in terms of price. Dealing with Bouchillon on the phone is not pleasant, unless rude and condescending are your type of guys. I bought one part from them online for which they were the only source (and wildly overpriced at that), and that was enough for me. I'll never deal with them again unless I simply can't avoid it.