Many thoughts! I'm currently a graduate student studying Shakespeare, but I've directed 5 productions of Shakespeare in non-academic environments.
First, I absolutely concur with the first responder's note that you should do fights right away. Your Hamlet has a lot of lines to learn, but he also kills three people onstage. The less your actor has to worry about that, the better.
Next, make sure to give adequate time for table work. The text isn't easy, and a lot of people have preconceived notions about it. I would give this a week, minimum. No less than 15% of your rehearsal time should be spent talking about the text, and I'd plan some late table rehearsals just to check in and have a chance to talk about the lines.
A good rule of thumb for staging rehearsals is 100 lines/hour. That's about 5 minutes of stage time. You may go faster in some scenes, slower in others, and you can feel that out. But use this as your baseline.
One of the best pieces of advice I ever received was to do 3 run throughs before tech. No more, no less. Give each one at least one work session in between. I like to do the first run immediately after I finish staging, before getting into the detail work. This doesn't include act runs, just full runs. It's enough to give ownership and a sense of flow, but not too much running without actively working the beats. Also with runs, if you don't require them to be off book from the beginning or before you stage, I like to allow actors their scripts until after that first stumble through.
Work in sequence as best you can, and don't neglect the transitions! Conflicts don't always allow this, but cut it up too much and they won't have a sense of the play.
I also recommend you break your script into beats (it seems you've already done that) and make sure not to interrupt your actors in mid beat. They don't even have to know about them, but giving them the chance to work through a problem is more helpful than fixing it immediately. I'm bad at this one, which is how I know it's so important.
So, to break it down, based on my advice:
Hamlet (2500 lines- assumed based on your 2.5 hour run time). This is also based on a 5 rehearsals/week, 4 hours/rehearsal schedule that I'm used to.
1.5 weeks - table work, including a read through, scansion, discussion of the text
Start fight rehearsals week 1, have 1 a week, minimum, as well as running a fight call any time all actors involved and a fight captain are present.
7 rehearsals - staging. This gives you a 3 rehearsal hour buffer on the 100 lines/hour rate I quoted. You'll need them!
Stumble through of the play. May be as many as 10 since it is a difficult play
Possible return to table for a rehearsal or two
Work through play again - 7-10 rehearsals, depending on how long you have your actors, and how long they have had their scripts. These should be off book
(Performance) act runs, with time at the beginning or end to work moments
Run show
work performance acts
Run show
Tech
Opening
Based on this, it is 27-33 4 hour rehearsals before tech begins, not counting fight rehearsals, so a 5-7 week process, before tech. I'd do off book after the stumble through, but that's my own preference.