Your onsite stay only includes the days you are actually staying onsite, including check-in and checkout days. It does not include days where you are staying offsite even if you are using the same ticket. So, you will not be able to book those later party days seven days before your check-in date.
However, I don't think you'll have to wait until three days before the individual party days. Doesn't your 14-day ticket have a start date? If it does, it is a dated ticket. See post 4290 on page 215 of this thread to see how onsite/offsite split stays work with dated tickets.
Note: edited to include reference to post 4290 to replace incorrect information.
Second edit: This answer is based on the fact the hotel you are switching to after leaving All-Star Sports is offsite. If onsite, different answer.
Thanks for the help, but I could use a bit more clarification. So, here are some specifics.
I have a 14 day Magic Pass (i.e. the UK hopper tickets) that is good for 14 park days during an 18 day period (8/31-9/17), dated to start on Aug 31, which includes water parks and mini golf (1 per day before 4PM) that don't actually count toward the regular park days.
I'm arriving on August 31, and checking in to All Star Sports for three nights. I'm visiting the WDW parks for four days while staying on property from August 31 to Sept 3. I'm also hitting the Mickey's Not So Scary on Sep 1 and the Hollywood Studios After Hours events on Sep 2 (as well as possibly Blizzard Beach and Winter Summerland Mini Golf on the 2nd as well), though none of that should affect this at all, since I'm also visiting those parks on those days and taking advantage of early entry. But I'm mentioning it in case there could be complications.
I check out on September 3 and am moving over to the Days Inn Orlando Conventions Center/I-Drive for the rest of my trip, since I'm mostly hitting the Universal and Sea World parks on those days.
On Saturday, Sep 12 (12 days after i arrive, and 9 days after my previous Disney park visit on this same ticket), I'm going back to Hollywood Studios for the whole day, mainly to take advantage of the short lines during the After Hours party. (I may also hit Typhoon Lagoon and the Fantasia mini golf earlier that day, depending on how I'm feeling, which, again, shouldn't affect any of this, but I'm mentioning it in case there's some weird situation where it does.)
Then, on Wed, Sep 16th, (16 days after I arrive, 13 days after my All Star hotel check out and previous contiguous park visit, and 4 days after the DHS visit), I'm going back to Epcot, mainly to take advantage of the short lines during the After Hours party. I may choose to hit DAK in the morning, depending on how much I managed to accomplish at both parks in the previous visits. But I almost definitely will hit Epcot earlier in the day, since I'm already going to be there and am paying for parking.
So, at 7AM on August 24th (7 days before my first park day and my check in), I can buy my LLMP's and make reservations for all four days from Aug 31-Sep 3, correct?
Then, at 7 AM on Sep 9 (3 days before), I can buy my LLMP for DHS on Sep 12, correct? Is there anything I have to do to make sure that their system knows that I'm coming back on that day and using the same 14 day ticket?
My big question involves the 16th. The post you quoted seems to imply that I can book LLMP for this day (the rest of the days on my ticket) along with the other LLMP on Sep 9. Is that true? Or would I have to wait for the 13th? Would the fact that this was 16 days after my arrival complicate anything? I know that you can only prebook all of your LLMP's for 14 day hotel stays. I'm not sure if this uses a different metric, or what.
Then, after all that, there's a further possible complication. (But I really hope it won't be!) I recently found some old tickets with some days on them. Guest services added those days as separate tickets to my My Disney Experience account. So, in addition to the 14 day Magic Ticket, I also have in my My Disney Experience account, a 1 day Magic Your Way park hopper ticket with no date or expiration. And also a 4 day Disney Water Park and Sports ticket, also with no date or expiration.
Is there any way that I can make sure that my 14 day dated Magic Ticket is the one linked/associated with this trip? I really don't want my LLMP purchase to be considered linked to the 1 day Magic Your Way ticket, especially if it could complicate buying LLMP as early as possible for the remaining three days. Also, I want to save that ticket for a future visit.
Similarly, is there any way I can make sure that the 14 day Magic Ticket is the one that is used when I use my Magic Band for park entrance on the park days?
Also, similarly, is there any way that I can make sure that that ticket is the one used at the water parks and mini-golf? I'd really rather not waste these days that I just found, since I'd like to use them for my next trip. (And I'm already not using the majority of the days I paid for with the 14 day ticket, but it was such a good deal - cheaper than a 5 day hopper ticket would have been - that it was worth it.) This is likely the biggest Disney trip I'm taking for quite some time, but I might take a smaller one in a few years, and could use those tickets. Am I better off just scanning the ticket directly in Google Wallet (or a downloaded scan), and avoiding the Magic Band for entry to be safe? Or is their system smart enough to use the tickets dated with those days?
Could there be any complications using the Magic Bands for Lightning Lanes with those three tickets in my MyDE account?
One last (hopefully, but I can't promise!) question: If I were to decide to stay on property for one night with those later visits (most likely for the Epcot day on the 16th, since the hotels are cheaper that day than on the weekend days surrounding my Sep 12 DHS visit), I assume that I could get LLMP 7 days before that stay?