Thanks for help guys, I had a look at the OneUp, unfortunately it's also a 125mm dropper with ~410mm overall length so that's about the same dimension as the Brand X.
Begbie I'm not sure I understood your question, the seatpost sticks up too much out of the seatpost clamp, there's 2-3" of seatpost housing between the clamp and the dropper's sealing collar. It does not go any further into the seat tube as the linkage bolt or bend get in the way. If I can get a dropper that is overall shorter by that much (the length from the cable clamp to the collar), that will solve the problem.
It looks like the project might be dead anyway because my girlfriend asked me not to get a new dropper, she'll deal with the current saddle height or put a normal post in.
FYI, if anyone looks at Small Transition Scouts, you'll never be able to run a dropper post slammed to the seat tube clamp.
Ok, just to help out there might be a way a different post will work. From what I understand, the Brand X 120mm dropper with the post all the way into the seat tube, means a seat height that's too high for your girlfriend? She shouldn't need to endure this, it'll make life uncomfortable. She could always look for some thicker pedals or shorter cranks, as this would effectively shorten the seat height, but there might another way.
As you've said the seat tube length on the bike is very short, the brand-x 120mm dropper is 229mm from bottom of the collar to the bottom of the connector. The Oneup 150mm is 255mm for the same measurement. So the Oneup Dropper would actually sit 100mm out the seat post, 25mm more. However...
Stack height is what's important. The Brand X has a stack height (bottom of collar to the seat rails) of 183mm. The Oneup (150mm remember) is 187mm. So based on the increased length of the insertion, that's now 29mm too high. Plus lets say 20mm that she needs to reduce the seat height by, so it needs to drop 50mm at full height. Well, that's what the Oneup Dropper can do. With the shim it'll go down to 100mm travel, so 137mm stack height.
So basically the OneUp post set at 100mm, even though it will have 25mm more of the post out the seat tube, will be 237mm from top of seat tube to saddle rails. The Brand X 120mm is 258mm from seat collar to saddle rails, so 20mm shorter. If you then found some thicker pedals, or maybe some thicker soled shoes, and maybe a lower profile saddle that could add another 10/20mm, or more. The only other option as you've said is to look for a 100mm or lower drop post.
Best thing to do is get the current dropper and adjust it so it's at the perfect height, then measure from the seat tube collar on the frame, to the rails. Once you know this figure you can see what might fit, and stack height is as important as insertion length.
HTH
Edit:
The Fox transfer 100mm could work. Insertion length inc actuator is 223mm, so that's 70mm post showing. Stack height is 161mm, giving total height above the frame of 231mm. Only a few mm different to the OneUp, but still shorter. You can see how the stack height is a very important number.
