My biggest suggestion to you is do not expect the suboxone to be a miracle and make you completely cured. It will make the withdrawals tolerable until the acute phase of w/d wears off, then you will just feel normal on Subs. The best reason to wait until in full blown w/d, IMO, is you will be able to tell the drastic difference form full blown heroin w/d to being on Subs while in H w/d. Obviously you don't want precipitated w/d's either, but the other issue is if you take it before you are really sick and dying, you won't get as much relief. Also start low, like 2 mg (I am sure you will need more, but who knows its possible you won't) and then add 1 mg every 2 hours until you feel satisfied with the relief. You have a small amount and want to make it work, so it is imperative to use as little as possible to succeed. If you take all 24 mg's in 24 hours they will wear off before long and you will be doing H again. Honestly, you really should consider seeing a Dr or getting more of those things, because you have a big habit and its going to be tough to stabilize and then wean off Subs with that habit.
But if not an option, in your case I would want to get through the first 3-4 days using only 2 of those strips. You can drastically reduce your dose at 2 points, 1 is once you have stabilized, that is after the 1st day when you do the induction. Lets say it takes you 6 mg to feel better, that was 6 from 0 in your system. Every other time after that you will need less because worth Subs long half life you have a good amount still in your system. Then there is the point where you are no longer in acute heroin w/d, after 4-5 days from last heroin use, at this point you should be able to drop your dose a good amount. So you would want to follow a system like this, day 1 6 mg, day 2 3mg, day 3 3 mg, day 4 3 mg, day 5 2 mg, day 6 1.5 mg, day 7 1.25mg, day 8 1 mg, day 9 1 mg, day 10 .75 mg, day 11 .5 mg, day 12 .5mg and jump This is quite a rapid taper and its assuming you can stabilize on a 6 mg initial dose. I honestly think even just having 1 or 2 more Sub strips in this situation makes it much easier. With 2 more you can start with a full 8 or 10 mg and you can make the wean a longer process which is more likely to work.
Also with your small amount you might consider some of the methods for potentiating, UTFSE and you will find plenty of info on that, whether it be the alcohol trick or different ROAs to improve bioavailability. Just factor in when you do it that way you are in essence doing more. So adjust a tapering schedule as necessary with the adjusted BAs.