AHC: Chilean Tierra del Fuego

In our timeline the southern Chile-Argentina border runs west to east before turning roughly east-southeast to Punta Dungeness, going across the Strait of Magellan, and then south down Isla Grande de Tierra del Fuego to the Beagle Channel. So is there any way to have the border instead continue running east to Cabo Virgenes and then out to sea, preferably with the minimum of fuss? Currently doing some reading about the history of the region but thought I'd see if anyone knew of a quick answer. Thanks.
The border is set like that so neither Chile can access the Atlantic Ocean nor Argentina the Pacific. During most of the XIX century Chile had a headstart in the colonisation of Patagonia, but had to divert efforts during the War of the Pacific, allowing Argentina to gain traction and seize modern borders. I guess the best way for Chile to succesfully claim and hold all of Tierra del Fuego would be make the War of the Pacific way shorter or avoiding it completely. Another way would be to give Argentina some extra political/foreign problems through the latter part of the century so the border demarcation is more favourable to Chile.