So I tried to follow more or less what you're doing here on my own.
I randomly selected picks for each of the Celtics' picks between 2014 and 2018, selecting within a range that seemed reasonable to me -- 25 to 35 wins this year, 25 to 45 wins next year, 30 to 45 wins the third year, and so on.
I did the same thing with the 2014 Hawks' pick, the 2015 Clips' pick, and the three Nets' picks (2017 being a swap option). I assumed the Philly pick turned into two second rounders. That means 9 picks over that 5 year period, with the right to swap picks with Brooklyn in 2017.
I took the players from the 2009 draft through the 2013 draft. I didn't bother doing the lottery, so I just assigned the picks based on where the win total fell in the standings (this only really made a difference once: the #3 pick in Trial 3 which in real life ended up at #5 for Sacramento). When there was a tie, I gave the tie breaker to my pick.
I also honored playoff standings, so a worse record in the East sometimes resulted in getting the #15 or #16 rather than a late lottery pick.
Here's what I got --
Trial #1:
2014 --> #7 Stephen Curry, #19 Jeff Teague
2015 --> #11 Cole Aldrich, #19 Avery Bradley
2016 --> #15 Kawhi Leonard, #7 Bismack Biyombo
2017 --> #12 Jeremy Lamb
2018 --> #16 Giannis Antetokounmpo, #15 Lucas Nogueira
Team #1
Curry / Teague
Bradley / Lamb
Leonard / Antetokounmpo
Biyombo
Aldrich
Trial #2
2014 --> #8 Jordan Hill, #18 Ty Lawson
2015 --> #12 Xavier Henry, #22 Elliot Williams
2016 --> #16 Nikola Vucevic, #9 Kemba Walker
2017 --> #9 Andre Drummond
2018 --> #22 Mason Plumlee, #7 Ben McLemore
Team #2
Lawson / Walker
E. Williams / McLemore
Henry
Vucevic / Hill
Drummond / Mason Plumlee
Trial #3
2014 --> #7 Stephen Curry, #15 Austin Daye
2015 --> #3 Derrick Favors, #28 Greivis Vasquez
2016 --> #15 Kawhi Leonard, #23 Nikola Mirotic
2017 --> #12 Jeremy Lamb
2018 --> #24 Tim Hardaway, Jr., #15 Giannis Antetokounmpo
Team #3:
Curry / Vasquez
Lamb / Hardaway, Jr.
Leonard / Antetokounmpo
Daye
Favors
A fairly mixed bag, as you can see. My methods are far from perfect, of course. I think it illustrates that even without many high picks, you can get a pretty good haul of talent. At the same time, you probably couldn't just go ahead and build a full competitive rotation out of 8 1st round picks over 5 years.
One factor worth mentioning here, of course, is that Danny may or may not be a better drafter than some of the GMs who chose the players that came up at certain spots in the sim. In many places there were probably better players available. It would be way too prejudicial to go ahead and play armchair GM with the benefit of hindsight, though.