Keep in mind I'm coming from a BBS experience with these coils so it could easily differ on FBS machines, but from all I've read at least the SEFs seem to work just as well on either Minelab...
I think your three best options are the 13" Ultimate, 12x10, or 15x12. Not sure how good the Ultimate is yet (still reading reviews) in hot ground, but by the sound of it it is probably as deep as the 12x10 and maybe deeper. I owned a 15x12 and it did seem to go deeper than my stock 10" in my mineralized beaches, but I'm not sure if it goes as deep on my beaches as my 12x10. I just know it's deeper than the stock 10" coil in my beaches. However, for some reason the 15x12 got less depth than stock in my soil sites, which range in minerals from mild to on the heavy side. In fact, I found that it will give better depth, or at least ID at depth, by lowering the sensitivity much lower than what was max stable...Probably due to the ground glare thing and washing out the target with the ground signal or something.
So, for that reason, while I would like to try the Ultimate I'm concerned it might be too big to show increased depths in my soil for the ground glare thing, even if it will run like the 15x12 (and 12x10) at high sensitivity. All these factors are based on your soil or sand. There is a certain limit in size to see gains in depth, not because of a larger coil losing sensitivity to coin or ring sized targets, but rather because they are just taking in too much ground signal and thus washing out the target or at least it's quality.
The 12x10 (like the 15x12) has such a tight/sharp field in the DD detection line width (less "fuzzy" field in general too) that I feel it actually rides on and sees less ground than my stock 10" round DD coil. And for that reason the 15x12 and the 12x10 will run at higher sensitivity levels than stock at the same sites, and false less, and runs smoother...But again size doesn't always translate into more depth. In general from what I've read over the years about 14" seems to be the max DD coil size to still see gains in depth on coin sized targets. About 10 to 12" for a concentric, as concentrics lose sensitivity on coin sized objects faster as they increase in size, not to mention in general ride on and see more ground matrix, so that alone limits them in terms of how big of a concentric you can go to depending on your soil.
But, as said, the 15x12 got more depth in my mineralized beaches than my stock 10" round coil and the coverage was awesome for gridding out areas faster. On the other hand, the 12x10 is still a nice improvement in coverage too. I'd ask others how the Ultimate does in mineralized soils or beaches and see if it seems to have a limit in terms of gaining depth in those situations. If that's the case then I'd lean towards the 12x10, because I believe it *might* be about the max coil size I can use and still see gains in depth in my soil and sand. I even have my doubts that a round 12" coil would get as deep as my 12x10 in my soils and sands, because these SEFs are riding on and seeing less ground matrix (glare). That gets more important as the mineral levels in your sand or soil rise. While some say the 15x12 gets more depth for them than a round 10" DD coil in their soil, in my land sites it did not.
Another thing to consider...The 15x12, like the 12x10 appears to me to be more sensitive to tiny targets than my stock 10" round coil. I've dug some pretty small stuff at some pretty amazing depths with both of these coils. But, the 12x10 appears a bit more sensitive and able to find small items such as earing backings, at least at greater depths. Probably because the official field test of the 15x12 versus the 12x10 found the 15x12 got less depth on coins a little smaller than a dime. I also know of a beach hunter that found a gold neckless with the 12x10 that was sure the S-12 wouldn't have hit as hard, and after some testing of the two confirmed that suspicion. Take that with a huge grain of salt, though, as I have never read any further comparisons of these two coils on small items to see if it is true or not one way or the other.
If you ditch the coil cover for one of the SEF coils and use spray on bed liner to protect the bottom (3 to 5 coats that dry well between them) you'll drop a good bit of weight off them, 'cuz those coil covers are rather heavy. The 15x12 without it's coil cover is lighter than my stock 10" coil with it's cover, and my 12x10 without it's cover is lighter than the legendary light weight of the S-12. However, we weighed a bunch of FBS and BBS coils and compiled a chart, and for some reason the FBS versions of the SEF coils are a good bit heavier than the BBS versions.
Hope all this helps, but as said take it with a huge grain of salt as I'm a BBS guy and can only speak to that end of these coils. I'm sure there will be FBS guys who chime in and correct any general statements I've made if needed. I'm just a big fan of these SEF coils, and hope to be a big fan of the Ultimate too, so I couldn't resist throwing in my two cents.