Depending on your stature, I suppose there will be a slightly higher chance of injecting straight into muscle which might speed up absorption rates. I think that's why in the earlier days when longer needles were standard we were encouraged to pinch up a fold of skin to take it further away from muscle. So, I'd maybe be inclined to pinch a bit more.
If there's a pharmacy open in the afternoon, I'm pretty sure they have ways of doing an emergency prescription and can then sort it out with your gp later. Have done that a couple of times when running low on strips, but it might depend on whether you've used that pharmacy before so that they've got your details on record.
Or I suppose you could just poke the needle half way in!