There is a Hep B series for your 2nd round that is only 2 shots:
Heplisav-B (HepB-CpG) vaccine as an option for incompletely vaccinated persons. This vaccination is only 2 shots 4 weeks apart. So you can get a shot and 4 weeks get a titer drawn. If negative, then get the 2nd shot and 4 weeks after the 2nd shot get a titer drawn. I HIGHLY recommend this series for you so you can get this completed in less than 10 weeks. This is best when you have to have your immunizations completed by July 1, including Hep B positive titers! (Non-responders would require 5-6 shot dates and 2 negative titers.)
Both doses have to be the HepB-CpG to do the 2 does option. You may still end up being a non-responder but after the 2nd Hep B titer we will know for sure.