You are really impressive, to keep trying despite some bad luck!
I must say that I didn't find Goat so difficult, but I think you are spot on that it is more luck-prone than other runs. Not only do you have to contend with the usual RNG-screwy nature of VGT's random punishments and the order of the exotic monsters, you have the additional RNG-screwy altar sequence.
That said, I would say that you should not need to be specifically *lucky* to Goat VGT; but rather, you should not be too *unlucky*, and you should have a decent shot at winning.
Not getting Dracul at all is a game ender, I mean it's really impressive that you got as far as you have!
That said, I don't think you need any special "help" against H., on my winning run I had items like Fine Sword, Pendant of Health, Mage Plate, Keg of Health and a Gloves of Midas (which afforded me the other items). Not the usual VGT-y stuff like the Platemail, Vampirict Blade, etc. I did find HALPMEH, though, which was very useful.
I'm cheering for you to get it done soon, you deserve your hard work to finally pay off!

"Thinker", just without the "ache".