Looking at the ratios for the six speed, it looks like first is too short, and second too long.
I think the ideal changeover setup in 113 manual cars is to fit a dog-leg Getrag box, with the 1:1 fifth, and then change the rear axle to a 3.27 or 3.46. But dog-leg Getrags are very hard to find, and expensive when you can track one down (and the only one I found had a cracked case and we sent it back) so I opted for a standard non-dog-leg box with the OD fifth, and we reinstalled the original rear axle with its 3.92 ring and pinion,or 4.08, whatever it is.