You're welcome, but I'm afraid that - at least until now - here you will not find a mathematical model for the best USB booting, but you can find only some thoughts about a success that until now the experts do not know to explain (and I even less).
well , after reading all three pages , im still confuse .. im trying to learn all those thoughts in it ./
All is started from my idea/observation that if your UFD is partitioned by XP's Disk Management in at least 2 (two) partitions than it will boot from reasonably the most machines (please, read: the most BIOSes) out there.
So, if your UFD already boots from your machine(s) and you are glad so, then you have not to do anything.
If you want to boot a your UFD that does not boot from a certain machine then you have to follow the suggestions of the real experts, and you have to ask to them.
If you want INCREASE your UFD bootability by yourself - just as I have done on all my UFDs and then I have been able to boot every my UFD from every machine I've tried (also from a machine that does not boot ANYTHING is not as a Hard Disk), because my "Format-it-&-Forget-it" way is able to do to see from the most BIOSes as a Hard Disk - than you can perform the way in my signature.
Here, and in the thread in my signature "Make Your Most Bootable USB Flash Drive"), we are talking about some evidences (discovered modestly by me ) that still have not a scientific explanation, if never they will have one.
However I had been glad to compare your attached MBR and I can see what is in the screenshot
I can just notice that the amount of zeros automatically selected by "010 Editor" above 55 AA bytes is small, but greater compared to HP Format Tool results (I think you have a single partition on your UFD).
I do not know to say more because I'm NOT an expert and I do NOT know even is this is a viable method, the only thing I can notice is that a smaller number of zeros automatically selected by "010 Editor" above the "55 AA" bytes seems to reach a better bootability.
And the amount of zeros automatically selected by "010 Editor" on my UFD partitioned performing my "Format-it-&-Forget-it" way is just null!
Please, note that it is a pure conjecture with nothing of scientific, and that most likely that conjecture is wrong.
Really the topic and the related observations are enormously unknown, then if you ask to the real experts I'm sure that they will know how to reply about a scientific method.
Sure, my "Format-it-&-Forget-it" way is the SIMPLEST way I know in order to highly increase your UFD bootability and it works much better for me compared or not compared to "all" known ways I've tried until now.
Sure, my "Format-it-&-Forget-it" way works on EVERY tried machine where HP Format Tool and/or other ways do NOT work.
Please, re-read the above notes about the real experts and their possible replies about a presumed and real scientific method.
Thank you for you post, really!