Sorry for the delay, weekends I'm out and about most of the day. Yes, the times are outside the parameters
pjf66 asked for, we had some PMs.
There are two options you could go with. Either way you would need to purchase two RT tickets: BOS/SEA and SEA/SJU. All miles are per ITA. Both options have several daytime hours in Seattle on the 13th outbound, a full day in San Juan, and 7 overnight hours in SFO returning.
--Option 1 total: $627.60 and 14,842 miles; 10 segments (3 on UA); total itinerary BOS-PHL-SEA-
SFO-PHL-SJU-PHL-SFO-SEA-PHL-BOS
--Option 2 total: $659.10 and 14,826 miles; 10 segments (1 on UA); total itinerary BOS-PHL-SEA-
PHX-PHL-SJU-PHL-SFO-SEA-PHL-BOS
Both of these leave room for a hotel night in San Juan while still being under your $800 budget; careful hotel pricing could give you rooms in both San Juan & SFO on the return where you wouldn't be afraid of the cock-a-roaches stealing your stuff, while still keeping within your budget.
I tried hard to get returns to BOS before 9:30pm (including back in BOS on the 15th) and/or departing BOS later than 5:30am, but had no luck finding options that would match both goals of 14.2k+ A3 miles earned
and $800 or less. I saw maybe 3-4 for around $850, and most were $900+, and still would have had at least one overnight connection somewhere along the line. Going through the LAX area instead of SEA was the next best option, many routings within budget, but either the mileage was short or routings required very tight transfers between airports. Someone who has been creating MRs longer than I have may have better success.
I could not get this to price out as a single booking online (couldn't even get all the city pairs in one whack), so it will need to be booked as two RTs. The BOS/SEA ticket can be purchased on the US site. The SEA/SJU ticket cannot be booked for those prices on the US site but can through Expedia, Orbitz and Travelocity using multicity booking. List SEA-SFO/PHX, SFO/PHX-SJU, SJU-SFO and SFO-SEA as the city pairs you want and limit carriers to US. The OTAs may offer other options with different departure/arrival times for the same or very close price.
When I verifed availability there were only a few left for either option.
Purchase the two RTs separately using your US FF number. Once confirmed & ticketed call US and see if you can have them combined to a single itinerary (for coverage in case of IRROPS). At checkin (or preferably before then) have everything switched over to A3.
NOTES:
--E fares earn 100% A3 miles on both UA and US. The US DM customer service guy I spoke to said US E maps to UA E.
--UA fares earn a minimum of 500 A3 miles on all discounted economy fares that earn A3 miles. US doesn't earn minimum A3 miles on any fare.
RT #1 BOS/SEA
October 13
BOS-PHL US1805, dep 5:30am arr 6:51a
PHL-SEA US82, dep 7:32am arr 10:19am
+++++
October 16
SEA-PHL US68, dep 11:15am arr 7:24pm
PHL-BOS US1408 dep 9:15pm arr 10:33pm
$301.20, 5300 miles
For +$85.00 you could take an earlier PHL-BOS flight on the 16th that lands at 9:30pm.
RT #2 SEA/SJU
October 13 Option 1
SEA-SFO US6418, dep 6:20pm arr 8:36pm (E fare, UA metal)
SFO-PHL US6518, dep 10:22pm arr 6:45am Oct 14 (E fare, UA metal)
October 14
PHL-SJU US1069, dep 7:40am arr 11:35am
October 13 Option 2
SEA-PHX US70, dep 5:30pm arr 8:21pm
PHX-PHL US1196, dep 10:45pm arr 6:08am Oct 14
October 14
PHL-SJU US1069, dep 7:40am arr 11:35am
+++++
October 15, same return on both options
SJU-PHL US1072, dep 2:45pm arr 6:36pm
PHL-SFO US667, dep 8:45pm arr 11:45pm
October 16
SFO-SEA US7578, dep 6:40am arr 8:43am (E fare, UA metal)
Option 1: $316.40, 9542 miles
Option 2: $357.90, 9526 miles
Personally I'd pick option 2. It puts all but one segment on US metal, which is safer for A3 earning. SFO-SEA would still be UA, but even if it maps to a 50% fare class the 500 mile minimum would kick in to make it 14,648 A3 miles.