Logic Masters Deutschland e.V.

This puzzle owes its existence to SudokuExplorer's 6x6 and 7x7 "Chaos Constructions: X-Sums" puzzles, which in turn were inspired by abed hawila. Inevitably, there was some discussion in the comments for these about making 9x9 grids using the same ruleset, and to my mind that sounded an awful lot like a challenge, albeit one that has since been met by other, more accomplished setters. Still, I'm historically bad at resisting the pull of a good challenge, especially when I'm supposed to be doing something else, so I started fiddling around with the concept - there's a fair bit I could say about the construction process, but all you need to know is that I stumbled across this clue layout entirely by accident and still can't quite believe how well it works. Well, by that I mean "there is a logical solution path that involves no true bifurcation, but blimey does it require some very interesting thinking"...

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Rules
The grid must be divided into nine regions, each consisting of nine orthogonally connected cells. Each row, column and region will contain the digits 1 to 9.
Numbers outside the grid have two functions. As X-Sums clues, they give the sum of the first X cells along their row/column in that direction, where X is the value of the first cell encountered. In addition, these clues guarantee that those X cells all belong to the same region, and that the (X+1)th cell does not. It is not necessarily the case that these eight clues are all the ones that could have been given.
The ninth clue is that the central cell, marked with a grey circle, contains an odd digit.
For examples of these rules in action, you can click through to any of the other X-Sums Chaos Construction puzzles referenced above and scrutinise their demonstration grids.

Solve with Penpa+ here! There should be automatic answer checking, 'cause it worked when I tested it, but it's the first time I've ever set it up so I can't comfortably guarantee it. Also, if you find yourself ground to a half after a decent spate of progress that's taken you halfway around the perimeter, this image might provide a hint... or it might just confuse things even further, let's be honest. Ah well. Good luck, and I hope you enjoy solving!