STL in 2001 has a pretty powerful set of CI/OFs: Albert Pujols (656), Mark McGwire (583), Jim Edmonds (393), Bobby Bonilla (287), JD Drew (242), Ray Lankford (238). Only problem is the six never start a game together, so the most you ever get is five - pretty sure every possible combination of 5 happens once, or at least most of them. The five that exclude JD Drew happened fairly often until Lankford was traded; that's 2157 HRs from your top five bats!
The biggest HR day of that team was on 7/6 at CLE, where they conveniently had the designated hitter; that starting lineup hit a massive 2503 HR for their careers, and left out only JD Drew. (Craig Paquette filled in as the sixth CI/OF/DH, adding his 99 career home runs to the 140 of Edgar Renteria, 40 of Fernando Vina, and 67 of eventual manager Mike Matheny, plus the 2157 above.
(If you're including anyone who makes an appearance in the game, then STL 2001 has some that all six of their big hitters appear in, plus Mabry or Polanco, which would add around 150 more to that total.)
However, this doesn't surpass 1995 CLE's normal starting lineup; that had 2669 HRs.
Even more astounding, you missed the player with the fourth highest home run total on that team. Belle only came in fifth; Dave Winfield was an occasional DH on the team, with 465 career HRs. On https://www.baseball-reference.com/boxes/CLE/CLE199505100.shtml for example, all five started; the team that day had 2,968 home runs by my calculations. That total is repeated a few other times that season, but never exceeded.
All of that, though, doesn't beat the Bronx Bombers of 2005. They had a killer lineup as well, led by Alex Rodriguez (696), Gary Sheffield (509), and Jason Giambi (440); but what sealed the deal was their middle infield, Derek Jeter and Robinson Cano, hitting for major power - 260 for Jeter and 324 for Cano. Most teams (like the aforementioned Indians) got nearly all of their power from the outfield and the corner infield, but the Yankees didn't have a player to hit for less than 175 career HR - and that was Hideki Matsui, who certainly would've hit for more in the MLB if he'd spent more time over here. In fact, you could easily add over 300 HR if you wanted to count all of his homers with the Yomiuri Giants
- but we won't for the purposes of this exercise.
On May 25, 2005, the starting lineup against the hapless Tigers hit for 3,305 career homers - none on that day, which is excusable since they probably were tired after going yard six times the day before.
One limitation of the python program I wrote to scrape this data is that it's quite hard to get information about pitchers, compared to hitters, due to some oddities of how Baseball Reference codes its (mostly easy to parse, except for this!) pages. So I decided to discard pitchers' totals, assuming it's unlikely that they'd make a difference, but will inspect any NL teams' totals that get close to the top in case it does.
Some followup: I finished running the program from 1969-present (something changed in the html formatting 1968->1969, and as I don't think there's any chance a pre-1969 team beats out the 'roid era I'm not going to chase it down right now), and think it's correctly handling pitchers now. No NL team gets into the top 25, unsurprisingly. The 2003 SF Giants are the highest NL team, just beating out 2001's STL and 2000's ATL with 2522 (ATL had 2514 and STL as noted above had 2503).
Counting only one appearance per year, here are the top 30:
Game number, date, opp, result HR# Team Year
------------------------------- ---- --- ----
46. Wed,5/25 vs DET W (4-2)# 3305 NYY 2005
24. Wed,5/2 vs BAL L (0-5) 3223 NYY 2012
158. Wed,9/27 vs BAL W (16-5) 3202 NYY 2006
5. Tue,4/5 vs MIN L (4-5)# 3178 NYY 2011
105. Mon,8/2 vs TOR L (6-8) 3043 NYY 2010
37. Sun,5/11 vs CLE W (17-10) 2992 TEX 2003
7. Sat,4/10 vs CHW L (3-7)# 2989 NYY 2004
13. Wed,5/10 vs KCR W (3-2)# 2968 CLE 1995
119. Tue,8/12 vs KCR W (9-0) 2876 CHW 2008
22. Sat,4/28 vs BOS W (3-1) 2837 NYY 2007
1. Tue,4/1 vs TOR W (3-2) 2837 NYY 2008
135. Fri,8/30 at SEA W (5-2)# 2821 BAL 1996
45. Wed,5/23 at TBD L (6-10) 2805 TEX 2001
56. Sun,6/7 vs TBR W (4-3) 2763 NYY 2009
137. Mon,9/2 vs CHW W (9-1)# 2753 NYY 2013
5. Fri,4/5 vs ANA L (1-3)# 2751 TEX 2002
48. Tue,5/27 at CHW L (2-8) 2743 CLE 1997
94. Thu,7/17 vs CLE W (5-4) 2720 NYY 2003
19. Tue,4/21 at ANA W (8-3) 2702 BAL 1998
1. Tue,4/2 vs NYY L (1-7) 2681 CLE 1996
5. Mon,4/11 at CAL W (9-6) 2674 CLE 1994
146. Thu,9/16 vs NYY L (5-9) 2611 CLE 1999
109. Fri,8/6 vs NYY L (8-11) 2582 SEA 1999
139. Thu,9/5 vs DET W (9-3) 2569 NYY 2002
101. Sat,7/30 at CHW L (2-4) 2564 SEA 1994
97. Sat,7/19 vs DET W (6-2) 2558 CHW 2003
141. Sun,9/6 vs BAL L (2-5) 2550 SEA 1998
38. Tue,5/19 vs NYY W (4-2)# 2540 OAK 1987
1. Mon,4/3 at BAL W (4-1) 2533 CLE 2000
110. Tue,8/13 at BAL L (7-8) 2527 TEX 1991
And just for fun, the bottom 20 - this is not the least home runs in a lineup, but rather the least most home runs in a calendar year (so this number here is the lineup with the most career HR, as of today, that team had in that year).
Game number, date, opp, result HR# Team Year
------------------------------- ---- --- ----
3. Mon,4/2 at TOR L (2-4)# 608 CHW 2018
2. Sat,3/30 at KCR L (6-8) 605 CHW 2019
63. Tue,6/13 at BOS L (3-4)# 604 PHI 2017
86. Sun,7/16 at BOS L (2-3) 595 MIN 1978
94. Sun,7/30 at HOU L (3-4)# 587 SDP 1972
50. Wed,5/31 vs STL L (4-5) 576 NYM 1978
82. Sun,7/3 vs NYM W (7-0) 569 SDP 1994
78. Wed,6/26 at HOU W (14-2)# 564 PIT 2019
45. Wed,5/30 vs OAK L (4-5) 552 MIN 1979
152. Tue,9/20 at MIL L (1-5) 545 SEA 1977
151. Fri,9/19 vs ATL L (3-12) 545 SDP 1969
9. Wed,4/15 at ATL L (5-7)# 542 SDP 1970
66. Wed,6/18 at KCR L (0-13) 537 CAL 1975
88. Sat,7/12 vs CHW W (7-0) 530 KCR 1969
144. Sat,9/7 vs TOR W (5-3)# 517 TBR 2019
95. Sun,7/18 at CIN L (0-3)# 493 SDP 1971
69. Thu,6/25 vs MIN W (4-1) 491 MIL 1970
26. Sat,4/29 at SFG W (12-4) 479 SDP 2017
19. Wed,4/29 at CIN L (5-8) 472 SDP 1981
Congratulations, San Diego Padres, you finally are the best at something!
And finally - here is the python file: https://github.com/snoopy369/Sports.SE/blob/master/hr_totals.py
Feel free to branch it and make it your own, maybe someone can fix the 1968-before pulls - I have no idea why those aren't working!