Total losses in case of 1100 kV line can be found as follows. As correctly commented below 3.5% loss per 1000km yields to 58.6% retained power over 15000km. So I will use 41.4% loss on that distance for my napkin calculation.

P_total = V_in * I_in, and P_loss = (V_in - V_out) * I_out

Since the charge flowing into the cable should exit on the other side I_in = I_out, then:

1 - V_out/V_in = P_loss / P_total = 0.414, and V_out = 0.586 * V_in = 468kV.

Voltage drop in 800kV line: V_in - V_out = 314kV = I * R (since lossses in DC lines are mostly due to heating, unlike AC lines where there is also capacity induced resistance).

Assuming that the same wires are used to transfer 1100kV DC current (i.e. resistance is the same) we can outline two cases:

A) you want to transfer the same inflow power on the Chilean side, then the voltage drop would be a 800/1100 fraction in comparison with 800kV line, i.e. V_in - V_out (1100kV case) = 314 * 800 / 1100 = 228kV. So the total loss is 20.7% (1.54% per 1000 km)

B) you want to transfer the same outflow power on the Asian side (i.e. smaller current due to lower voltage), then the voltage drop would be 162kV (there is a simple quadratic equation, if instead of considering inflow powers, one considers outflows which depend on V_out), so the total loss is 14.8% (1.06% per 1000 km)

Summary: same (as in 800kV line case) inflow power on Chilean side - 20.7% loss, same outflow power on the Asia side - 14.8% loss.