Sounds like a bit of a newbie question!!

I'm doing up my Dad's old '91 Saracen and I've got an old Octalink Strongarm chainset knocking around that I'm going to fit. So I've taken out the old cup & cone BB and last night as part of fitting a BB to another frame I tried it for size on the Saracen.

Now I've fitted quite a few cartridge BBs over the years and always used to half install the non-drive side adaptor before fitting the main driveside unit. Last night I followed Shimano's instructions and fitted the main unit first. On both frames it was really hard work to get the main unit in and then I couldn't get the adaptor to fit in (the axle wasn't centred).

Next I tried half installing the non-driveside adaptor and while it worked fine on my other frame I couldn't get the tool to fit in the adaptor for the Saracen.

I'm wondering whether its possible to almost fully install the non-driveside adaptor before the main unit? I don't particularly want to spend money on an octalink BB and find I can't get it to fit.