MHO
Remove ALL old glue from that broken seam. That includes all the excess glue on the
inside of the shell. That extra glue has a very brittle quality to it and it will pop off fairly easily with a small chisel. It adheres excellently to the wood fibers, as you may see it pull off surface fibers of the wood as you chisel it off. From the photos you can see that the old glue, on the inside of shell, spans across the broken seam on the outside of shell. This may be preventing you from closing up the seam totally when clamping.
Also you can see little bumps of old dried glue on edges of broken seam. Make an effort to clean that up
totally with sandpaper. Again, all those little hard bumps can cumulatively make it difficult to close up the seam.
Get your clamping apparatus together and practice clamping with a "dry fit". This will give you a little foretaste of what to expect: how much pressure will be needed to close up seam (or if it is even possible), and whether or not your clamping set up is adequate for the job. All this without having the complication or urgency of having to deal with messy glue at the same time. The dry run will tell definitively how wide a glue line you will end up with, and help make a decision as to whether or not to use a spline.
For a wide (Re)glue line I prefer a spline or shim.
Jerry Bembe wrote:Filler will be your safest bet. Use a filler that has a glue quality. If it shrinks then use epoxy to fill the fine cracks from shrinkage. Epoxy is the strongest glue to use but it can be messy.
I beg to differ. Filler is filler, it is NOT glue.
Epoxy glue has a property other wood glues do not: it is "gap filling", that is, it can retain 100% of its glue strength across a gap, thereby enabling one to have a strong joint with a wide glue line. Wood glues (like TB3) don't have these properties, and rely on close wood to wood contact on the joints.
The problem with most commonly available epoxies is that they are thin and "runny", and gravity may cause it to run out of the joint, unless the glue is contained. There are thixotropic agents like cabosil which thicken the mix and actually make it stronger, but ususally color the resin translucent white (the color of the cabosil).
It all boils down to aesthetics. Would you mind a big fat glue line?
If not, a spline or shim may be an alternative, but in order to get aesthetically pleasing results would require additional steps. The wood for the shim should be of the same variety as the existing shell wood, which is Luan, also known as Philippine Mahogany...but not really Mahogany.
As you can see from the pic of your shell, Luan varies greatly in color, even showing through the stain on your shell. The best results for overall finish would be achieved by stripping stain from shell, then glueing / shimming / repairing crack / sanding shim to be fair with shell surface, and then re-staining. By doing all the above you could end up with a very un-obtrusive repair, that blends in with the overall tone and color of the stain on the wood.
The shimming is a matter of individual fitting. After you have "dry fit" clamped your shell, the idea is to make the shim as thick as the remaining visible gap. It may take some tedious sanding and fitting to get it right (a beltsander is a must), but is time well spent. The more actual real wood you can use to fill the gap, the less it will look like a fat glue line.
For all these repairs I favor standard wood glue like Titebond3. As long as you can get get close fitting joints, it is more than strong enough, and cleans up with water.
If you have never used epoxy, I would not recommend it for your first try on a conga shell clamp-up.
Try practicing with it to get use to it's messy characteristics.
Again it gets down to aesthetics, do you want to just get it back together and functional again, or do you want to do a "restoration". Restoration work is a more time consuming.