I wouldn't worry about not hitting 15 reps on your second set, just keep going until your reps start to slow & stop (thereby avoiding failure).
If you're in the second week of 15s and you're close to failure on the first step then just repeat your weights until the last couple of sessions when you can increase it so the last one or two you're doing 15 pretty much to failure...this may be a weight that's less than your originally planned 15rm but this really doesn't matter. In the 10s I would just progress from the weight you finished the 15s on (so your first 10s workout may be with your originally planned 15rm max) and carry on from there.
The main thing is that generally the weights are going up and you're not training to failure (apart from maybe the last one or two sessions of 15s/10s etc), you don't have to hit your maxes at the end of each microcycle. When I change exercises for a new one I don't establish rep maxes, I just start from a reasonably low weight I think will still stimulate a growth response (i.e. not ridiculously light) and increase the weight every session, if I end up dong 12 reps on the last day of 15s it doesn't matter at all, I might repeat weights for a couple of sessions if the number of reps I can do is going down too quickly just to keep all exercises at the same point in the cycle but it's not a big issue.
Personally I don't see any reason to sd and start again having testing your new maxes, the 15/10/5s is not an essential part of hst, it's just an easy framework to plan your workouts around.
Hope that helps
Cheers
Rob