When during your upkeep can you cast upkeep spells?
Here's a thread on BoardGameGeek where people discussed this very question:

http://boardgamegeek.com/thread/530872/upkeep-adjusting-skill-sliders-and-casting-spells

The thing everybody agrees on is that spells are cast after the 'Refresh Exhausted Cards' step. Whether or not you're allowed to cast spells after moving skills sliders is debateable. An interesting point that is brought up is that Upkeep spells (at least until the reprint of Curse of the Dark Pharaoh) said


  Upkeep: You may cast and exhaust...


compared to other spells which said


  Any Phase: Cast and exhaust to....


Which makes me believe that these cards have the following rule from the rule book apply (bolded words are my emphasis)


  Perform Upkeep Actions
  
  After refreshing his exhausted cards, each player must
  review his investigator’s cards to see if any of them
  have an Upkeep action. Each player must perform all
  Upkeep actions listed on his investigator’s cards every
  turn. Upkeep actions may be taken in any order the player wishes. Bless, Curse, Bank Loan, and Retainer cards
  do not require an upkeep roll during the first Upkeep
  Phase after an investigator acquires them.Each player must perform all
  Upkeep actions listed on his investigator’s cards every
  turn.


Since the spells have Upkeep: on them, they count as upkeep actions (much like Blessings, Curses, Retainers, and Bank Loans) and have to be used during the Perform Upkeep Actions step, but they have the may qualifier on them they don't have to cast. Fantasy Flight just got lax with the Upkeep spell verbiage in later expansions I guess.

But really, as long as you aren't casting/refreshing/recasting spells during upkeeping you're good.

EDIT:

I should clarify that I'm not really a strong proponent of the specific logic in the argument above, I was just summarizing the thread I linked to. It seems like a nice idea but causes too many issues when you find Upkeep spells that lack the word 'may'. 

A similar argument is that you have to use the evade bonus from a dark cloak when making evade checks because there's nothing that says you have the option of not using items. (Example situation: If you wanted to take combat damage and get sent to the hospital without having to make a horror check). I find forcing Investigators to use items in any situation where they could be applicable to be a bit extreme. This would fall under that same category for me. Personally, when Fantasy Flight said 


  must perform Upkeep actions listed on his investigator's cards


I read it as


  may perform any Upkeep actions listed on his investigator's item cards and must perform any Upkeep actions listed on his investigator's non-item cards


since I don't think manditory item use is reasonable. If you believe that item bonuses are non-optional, then casting spells during upkeep would be non-optional as well.

EDIT 2:

As far as the the timing of the actions go (since that was actually what the question was about) the rules say this about the Refresh step (emphasis mine):


  At the start of the Upkeep Phase, each player
  refreshes...


and this about the Adjust step (as you've noted) (again, emphasis mine):


  Finally, each player may adjust...


This would suggest that, within the Upkeep Phase, nothing can come before the refresh step and nothing can follow the adjust skills step. Thus, spells would have to fall someplace in the middle, regardless of them being mandatory or not. You could however interpret "finally" as simply denoting the last item in a list rather than meaning "At the end of upkeep phase", but I think it's pretty clear that the Refresh step is the very first thing that happens.