Interesting points, Burglar. Just a few observations, admittedly with a designer's bias.
Yes, draws can happen at Morelli - which, btw, I consider a plus in a game, not a minus, as long as they're interesting draws and the incidence is low. But thus far (and I'm talking about all plays here, not just LG) draws on 9x9 are running at around 5% (which seems reflected at LG too). At 11x11, negligible: as far as I'm aware, just two draws ever anywhere, including, as it happens, your recent game against Russ. And at 13x13, again as far as I'm aware ... a still-intact virginity :)
So I don't really think - no, I really don't think - that Morelli could be said to be drawish, even at 9x9. (I might add, incidentally, that in my view of things the 'real' game is and always has been 13x13. Until the Boardspace implementation came along, I only ever thought of 9x9, and even 11x11, as, so to speak, stepping-stones to the full rainbow - and I was amazed when 9x9 turned out not to be not that trivial at all. Amazed, and gratified, except for the unintended consequence that quite a lot of people seem to start with 9x9 and then look no further, which I'm rather sad about. I do hope more players here will explore the (very great) delights of 13x13 once they get used to the game.)
As for a 'draw offer' button, though - well yes, I do think that might make sense, though I hope it wouldn't lead to too many deals in situations which needn't have led to draws at all.
Finally, the corner cells. It's true that pieces can't escape from a Great Diagonal, but the obvious disadvantage of that is balanced by subtle advantages which gradually reveal themselves with time - notably as a means of escaping zugzwang situations. These are very numerous at Morelli (Carroll just ended up losing an epic to you in precisely that way), and the game which you and I have just completed is a perfect example. I had the Centre, but was in danger of having to dismantle my block against your retaliatory corner square unless (the only hope) I could freeze the whole diagonal. So it was a battle between me, fighting to get myself trapped, and you, fighting to stop me. Talk about role reversal!
So, in a nutshell, I believe that experience has definitely shown the management of the corners and diagonals to be an integral part of the richness of the game, and I'm as sure as I can be that the sorts of measure you suggest aren't necessary - because there really isn't a problem. I do hope you'll come to see it that way too.