A few thoughts
Rest between singles, as long as they are not maximal doesn't have to be super long. If i was doing that program up to 90% of max i'd probably do a few warmups at a lighter weight and then attempt to do 2-4 singles with 30 seconds rest between each rep then maybe a 1-2 minute break and another 2-4 singles etc. I wouldn;t attempt to work up to a max every session. Either do 8 singles (or doubles) across at the same top weight, perhaps start with 80% of max and try to add a little each session until you hit 90 - 95% of your old max for 8 singles. At that point your old max will not be your max and you'll need to figure out your 1RM again.
Doubles, much the same except say do 2 doubles then rest a little longer and repeat.
Front squats - rest approx 2 minutes between sets. I'd do these a little differently. first two sets as the warm up then 3 x 5 at working weight with an extra 5kg on the last set IF you are feeling good.
Presses as for squats - presses don;t normally need a lot of rest between sets until you go really heavy