I am being optimistic.
Yes, and I see that you're getting that same advice on the TA forum. Rome alone will fill the 2.5 days. No way I'd try to do the Vatican, Colosseum and Borghese in a single day, and especially not in the August heat and humidity. Also, be sure you're working with days you know for sure both the Borghese and Vatican museums will be open, and understand that you're going to need to make advance, timed-entry reservations for both + the Colosseum. You are a bit late in the game for next month's tickets so you'll want put the giddyup on.
Colosseum: check the coopculture website for the next dates that timed, ordinary entrance tickets go on sale. This is THE #1 attraction in Rome and tickets can sell out very quickly when they become available. Ordinary entrance tickets do not include a guided tour; they do include entrance to the Palatine/Forum as well.
CALENDAR WITH THE GRADUAL RELEASE DATES OF TICKETS WITH SCHEDULED ENTRANCE OF THE COLOSSEUM
DAILY OPENING
Every day at 3.00 pm (UTC+1) new tickets for the next day
WEEKLY OPENING
Every Monday at 6.30 pm (UTC+1) new tickets for the following week
https://www.coopculture.it/en/colosseo-e-shop.cfm
Monthly and Quarterly release dates for August have already passed but you can check and see if there are any remaining openings or just wait for the next weekly release.
For a bargain-priced tour of JUST the colosseum, this is also a possibility depending on your dates. It doesn't include the underground but the ticket does include entrance to the Palatine/ Forum (highly recommended):
https://ecm.coopculture.it/index.php?option=com_snapp&view=event&id=E6A1B5B3-BFDA-AC94-6929-0161B2E3A0C0&catalogid=BDB46B8C-0C49-10F2-6036-0167A8502B26&lang=en
Very reasonably priced guided tours of the Vatican are possible through the Vatican's own website as well unless your dates are already booked. Note that "open tour" means a general entry ticket and no guide
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/visitatori-singoli.html.
Or you can, as suggested, look at tours provided by Walks of Italy or The Roman Guy: both highly recommended by RS posters who've used them. Dark Rome is another possibility.
And, of course, Rick offers some self-guided tours which can be downloaded to your own devices but you're already aware of those. :O)