Right. You have options here. I had a similar issue with my 1949 Higgins and, as it was pretty much a historic frame decided to stay with the OLD it had and go for single fixed. All well and good, but not ideal for all circumstances. I have other bikes, so that is a luxury I can afford. I ride it in perfect conditions whenI am fit enough to cope, and that is not often!
It would be perfectly possible to get a 4 speed into that OLD. Your problem would be finding a 4 speed block in reasonable condition to use. I has been a while since they were made and they are scarce in any condition. It would not be difficult, I think, to push your OLD out to 120. This would make 5 speed possible and there are 5 speed blocks available. From my experience, steel frames bend quite easily and the only problem you have is the angle that the clamping wheel nuts meet the frame. Use the "cold setting" method and use spacers to get the OLD you need. Even 125, if you need it is not beyond reach.
1949 Higgins Ultralite fixed wheel
1959 Sid Mottram (Mercian)
1963 Viking Severn Valley
1979 Viking Vision
(Oh, and 2013 Bianchi Sempre - winter bike!)