Greetings, fellow traveller.
I am sorry to say, but I am too lazy to go through your calculations.
Instead I would like to direct you to this little database on PFSRD.
It does all what you asked for (although, to reproduce your example and add 4 HD to a medium giant spider my browser crashed three times...).
Ruyan.
Creative Director
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Advancing a Medium giant spider to Huge size does indeed give it +16 STR and +8 CON. This also will result in a pretty different spider than the one in the 3.5 Monster Manual, but that's fine.
FIRST POINT: The "Giant Creature" simple template is meant to be a simple solution. One you can use on the fly, without having to go through all the following rebuilding steps. It's not one you should use at all if you're manually rebuilding a monster for a larger size category.
Now then.
For many of the vermin in the Bestiary, we provided a handy table as a guide for advancing them to different sizes; the way we arrived at those HD and CR ranges was by going through the following process.
First, advance its bite damage by two categories (from 1d6 to 1d8 and then to 2d6), which with its increased strength would give it a bite attack of 2d6+12, for an average damage per bite of 19 points.
Look at Table 1–1 in the Bestiary and find where that 19 points sits comfortable between the average damage ranges. Looks like CR 5 or CR 6. Since the Huge Ogre Spider from the giant spider table pegs it at CR 5, we'll stick with that.
According to Table 1–1, a CR 5 monster should have about 55 hit points. The Huge spider currently has a Constitution of 20, so that gives it +5 hp per HD. Start plugging in HD amounts. When we get to 6 Hit Dice, we get 6d8+30 Hit Dice (average of 57 hp). When we go to 7 Hit Dice, that gives us 7d8+35 HD (average of 66 hp).
Now we look at the Huge spider's armor class. Going from Medium to Huge gets the spider a net total of +5 to its natural armor class, according to the table in the Bestiary, but going from Medium to Huge also gives it a total of –4 Dex and an additional –2 size penalty from size, which results in an overall change to AC of only +1. Which, when we adjust things to the Medium spider's baseline gets an AC of 15, which according to Table 1–1 is 3 points too low for a CR 5 creature.
At 7 HD and 20 Con, its poison save DC becomes DC 18, which is kind of high for a CR 5 creature. It's attack roll for its bite attack is (base attack +5, +8 from Str, –2 from size) is +11, which is just barely above the expected +10 for a CR 5 creature.
It's a vermin so it has a good Fort save. At 7 HD, that sets its base saves at +5/+2/+2; applying its stat mods gives us Fort +10, Ref +3, Will +2.
At this point, I would make a judgment call; a low AC more or less balances with high hp, which gives us these baseline stats for the Huge Spider:
CR 5
AC 15 (lower than average)
HD 7d8+35
hp 66 (higher than average)
Attack roll +11 (slightly higher than average)
Average Damage 19 points (within expected rage)
Poison save DC 18 (higher than average)
Good saves Fort +10 (higher than average)
Bad saves +3/+2 (both lower than average)
When you look at this as a whole, we see a monster that's easy to hit but has a lot of hit points, does better than most for its good save but worse on its bad saves, hits pretty much as often as you'd expect and does as much damage as you'd expect but packs a stronger than expected punch with its poison.
It has a few other disadvantages that shouldn't be overlooked; it can't fly (which, against an average party level of 5 could be a HUGE disadvantage), but more importantly, it's mindless. This makes it immune to mind affecting attacks (and helps to ameliorate its low Will save), but means that it not only has no feats or skill ranks, but that it won't use smart tactics and can be outsmarted by pretty much everything.
Looks to me like a pretty solid CR 5 creature.
ADVANCED TOPICS
1: Since the spider's HD went from 3 to 7, it gets a +1 bonus to an ability score. Since it's AC is so low, I would put this into its Dex; raises its AC and reflex save by +1, which brings its reflex in line with average and its AC closer to the expected total.
2: I like to take things further than simply advancing a monster's stats. It's more interesting to me if this new monster isn't just a Huge version of the giant spider, but instead it's own species. The best way to make it its own species is to give it a new special attack or defense that the baseline spider doesn't have. Looking at real-world spiders gives us LOTS of choices; some spiders can fling poisonous hairs from their bodies, some are very adept at hiding, some have unusually powerful bites, some can do really amazing tricks with webs (such as using them to glide or as bolas). Alternatively, you can give the new spider an interesting universal monster rule; say "grab" with its bite or perhaps Spring Attack as a bonus feat.
3: While this Huge spider's poison DC went up, changing what the poison actually does is another relatively easy way to make the Huge spider its own thing. Giant spiders normally do Strength damage with their bite, but you could change the Huge spider's poison however you want. Increasing its duration to 6 rounds from 4 is also a good idea, since poison that lasts for 4 rounds is not the norm (it's something we normally give to low CR monsters because poison at low CR is kinda mean).
DISCLAIMER
I did most of this in my head, so there may be a few errors in my above calculations, but hopefully the thought process proves helpful anyway! Advancing monsters by hand isn't a simple task, but complexity isn't always a bad thing. IN any event, one of the things we'll be doing in Bestiary 2 and beyond is providing pre-built larger/smaller vermin for GMs to play with; we do the same in most of our adventures. So eventually, we'll have LOTS of pre-built vermin stats in print.