36V open-circuit is a bit low, double that would be perfect. Older AC welders had 60-70V O/C, newer ones keep it below 50V as this is considered the maximum safe touch voltage but that is pretty marginal for welding with. How are you regulating the current now? Did you leave the magnetic shunts in? Your options for current regulation are:
1) Movable magnetic shunts
2) A seperate limiting choke (on primary or secondary), with either an adjustable gap, multiple taps or a DC control winding.
3) Series resistance somewhere, see below.
4) Fancy electronics.
DC welding can be done on lower voltages, I found 24V unusable for any but the smallest rods and 36V to be about right :-). To convert to DC you'll need a high current rectifier (easy/cheap) and a *big* smoothing inductor (much less so). I used 3*12V flooded lead acid batteries, current limiting was a length of very heavy fence wire and a sliding croc clip. The whole thing was packaged in a large wooden crate with a homemade 230V-36V charger and it allowed me to do big welding on a very limited 2 kW supply so long as the duty cycle was low enough to keep the batteries topped up.