Good point about the origin station already having a delay in the reply I posted earlier....I missed that.
It looks like this is the winner for the train departing on-time having the biggest delay:
History for Amtrak 1 originating 02/06/2012 (Mo)
* THIS TRAIN EXPERIENCED A SERVICE DISRUPTION.
* Sunset Limited
* Eng: 90
* +---------------- Station code
* | +----------- Schedule Arrival Day
* | | +-------- Schedule Arrival time
* | | | +----- Schedule Departure Day
* | | | | +-- Schedule Departure Time
* | | | | | +------------- Actual Arrival Time
* | | | | | | +------- Actual Departure Time
* | | | | | | | +- Comments
* V V V V V V V V
* NOL * * 1 1155A * 1155A Departed: on time.
* SCH * * 1 125P * 131P Departed: 6 minutes late.
* NIB * * 1 251P * 319P Departed: 28 minutes late.
* LFT * * 1 319P * 351P Departed: 32 minutes late.
* LCH * * 1 450P * 536P Departed: 46 minutes late.
* BMT * * 1 643P * 710P Departed: 27 minutes late.
* HOS 1 913P 1 950P 956P 1016P Departed: 26 minutes late.
* SAS 2 300A 2 540A 424A 543A Departed: 3 minutes late.
* DRT * * 2 835A * 558P Departed: 33 hours and 23 minutes late.
* SND * * 2 1110A * 842P Departed: 33 hours and 32 minutes late.
* ALP * * 2 124P * 1034P Departed: 33 hours and 10 minutes late.
* ELP 2 415P 2 440P 125A 140A Departed: 33 hours late.
* DEM * * 2 611P * 319A Departed: 33 hours and 8 minutes late.
* LDB * * 2 706P * 407A Departed: 33 hours and 1 minute late.
* BEN * * 2 911P * 610A Departed: 32 hours and 59 minutes late.
* TUS 2 1040P 2 1130P 716A 754A Departed: 32 hours and 24 minutes late.
* MRC 3 1247A 3 1257A 928A 1140A Departed: 34 hours and 43 minutes late.
YUM * * 3 344A MST
PSN * * 3 454A PT
ONA * * 3 646A PT
POS * * 3 656A PT
* LAX 3 830A * * 757P * Arrived: 35 hours and 27 minutes late.
And here is the train that had the most delays enroute (35 hours, 42 minutes) after subtracting the initial 14 minute late departure.
History for Amtrak 6 originating 03/12/2019 (Tu)
* THIS TRAIN EXPERIENCED A SERVICE DISRUPTION.
* California Zephyr
* +---------------- Station Code
* | +----------- Schedule Arrival Day
* | | +-------- Schedule Arrival Time
* | | | +----- Schedule Departure Day
* | | | | +-- Schedule Departure Time
* | | | | | +------------- Actual Arrival Time
* | | | | | | +------- Actual Departure Time
* | | | | | | | +- Comments
* V V V V V V V V
* EMY * * 1 910A * 924A Departed: 14 minutes late.
* RIC * * 1 922A * 935A Departed: 13 minutes late.
* MTZ 1 954A 1 954A 1000A 1004A Arrived: 6 minutes late. | Departed: 10 minutes late.
* DAV * * 1 1036A * 1046A Departed: 10 minutes late.
* SAC 1 1058A 1 1109A 1102A 1113A Arrived: 4 minutes late. | Departed: 4 minutes late.
* RSV * * 1 1135A * 1140A Departed: 5 minutes late.
* COX * * 1 1221P * 1240P Departed: 19 minutes late.
* TRU * * 1 238P * 253P Departed: 15 minutes late.
* RNO 1 356P 1 406P 348P 407P Arrived: 8 minutes early. | Departed: 1 minute late.
* WNN * * 1 708P * 708P Departed: On time.
* ELK 1 931P 1 931P 908P 933P Arrived: 23 minutes early. | Departed: 2 minutes late.
* SLC 2 305A 2 330A 248A 330A Arrived: 17 minutes early. | Departed: On time.
* PRO * * 2 435A * 435A Departed: On time.
* HER * * 2 637A * 640A Departed: 3 minutes late.
* GRI * * 2 759A * 808A Departed: 9 minutes late.
* GJT 2 1011A 2 1023A 1008A 1025A Arrived: 3 minutes early. | Departed: 2 minutes late.
* GSC * * 2 1210P * 1232P Departed: 22 minutes late.
* GRA * * 2 312P * 353P Departed: 41 minutes late.
* WIP * * 2 350P * 431P Departed: 41 minutes late.
* DEN 2 638P 2 710P 725P 424A Arrived: 47 minutes late. | Departed: 9 hours, 14 minutes late.
* FMG * * 2 825P * 621A Departed: 9 hours, 56 minutes late.
* MCK * * 3 1249A * 346A Departed: 3 hours, 57 minutes late.
* HLD * * 3 154A * 846P Departed: 19 hours, 52 minutes late.
* HAS * * 3 242A * 950P Departed: 20 hours, 8 minutes late.
* LNK 3 320A 3 326A 1133P 1244A Arrived: 20 hours, 13 minutes late | Departed: 21 hours, 18 minutes late.
* OMA 3 459A 3 514A 1127A 1223P Arrived: 30 hours, 28 minutes late | Departed: 31 hours, 9 minutes late.
* CRN * * 3 704A * 537P Departed: 34 hours, 33 minutes late.
* OSC * * 3 740A * 626P Departed: 34 hours, 46 minutes late.
* OTM 3 900A 3 909A 810P 820P Arrived: 35 hours, 10 minutes late | Departed: 35 hours, 11 minutes late.
* MTP * * 3 954A * 1004P Departed: 36 hours, 10 minutes late.
* BRL * * 3 1036A * 1036P Departed: 36 hours late.
* GBB 3 1141A 3 1141A 1153P 1203A Arrived: 36 hours, 12 minutes late | Departed: 36 hours, 22 minutes late.
PCT * * 3 1233P CT
* NPV * * 3 153P * 211A Departed: 36 hours, 18 minutes late.
* CHI 3 250P * * 246A * Arrived: 35 hours, 56 minutes late.
Here's an honorable mention...it left the origin 1 hour, 22 minutes late:
History for Amtrak 5 originating 06/26/2015 (Fr)
* THIS TRAIN EXPERIENCED A SERVICE DISRUPTION.
* California Zephyr
* +---------------- Station Code
* | +----------- Schedule Arrival Day
* | | +-------- Schedule Arrival Time
* | | | +----- Schedule Departure Day
* | | | | +-- Schedule Departure Time
* | | | | | +------------- Actual Arrival Time
* | | | | | | +------- Actual Departure Time
* | | | | | | | +- Comments
* V V V V V V V V
* CHI * * 1 200P * 322P Departed: 1 hour, 22 minutes late.
* NPV * * 1 234P * 402P Departed: 1 hour, 28 minutes late.
* PCT * * 1 344P * 513P Departed: 1 hour, 29 minutes late.
* GBB 1 438P 1 438P 622P 654P Arrived: 1 hour, 44 minutes late. | Departed: 2 hours, 16 minutes late.
* BRL * * 1 525P * 905P Departed: 3 hours, 40 minutes late.
* MTP * * 1 559P * 941P Departed: 3 hours, 42 minutes late.
* OTM 1 653P 1 653P 1128P 646P Arrived: 4 hours, 35 minutes late. | Departed: 23 hours, 53 minutes late.
* OSC * * 1 809P * 909P Departed: 25 hours late.
* CRN * * 1 841P * 1213A Departed: 27 hours, 32 minutes late.
* OMA 1 1055P 1 1105P 517A 606A Arrived: 30 hours, 22 minutes late | Departed: 31 hours, 1 minute late.
* LNK 2 1208A 2 1214A 716A 754A Arrived: 31 hours, 8 minutes late. | Departed: 31 hours, 40 minutes late.
* HAS * * 2 147A * 926A Departed: 31 hours, 39 minutes late.
* HLD * * 2 234A * 1019A Departed: 31 hours, 45 minutes late.
* MCK * * 2 343A * 1125A Departed: 31 hours, 42 minutes late.
* FMG * * 2 505A * 145P Departed: 32 hours, 40 minutes late.
* DEN 2 715A 2 805A 322P 529P Arrived: 32 hours, 7 minutes late. | Departed: 33 hours, 24 minutes late.
* WIP * * 2 1007A * 830P Departed: 34 hours, 23 minutes late.
* GRA * * 2 1037A * 915P Departed: 34 hours, 38 minutes late.
* GSC * * 2 153P * 104A Departed: 35 hours, 11 minutes late.
* GJT 2 357P 2 410P 256A 313A Arrived: 34 hours, 59 minutes late | Departed: 35 hours, 3 minutes late.
* GRI * * 2 558P * 504A Departed: 35 hours, 6 minutes late.
HER * * 2 720P MT
PRO * * 2 926P MT
* SLC 2 1105P 2 1130P 950A 1013A Arrived: 34 hours, 45 minutes late | Departed: 34 hours, 43 minutes late.
* ELK 3 301A 3 303A 151P 159P Arrived: 34 hours, 50 minutes late | Departed: 34 hours, 56 minutes late.
* WNN * * 3 540A * 540P Departed: 36 hours late.
* RNO 3 825A 3 836A 814P 855P Arrived: 35 hours, 49 minutes late | Departed: 36 hours, 19 minutes late.
* TRU * * 3 937A * 954P Departed: 36 hours, 17 minutes late.
* COX * * 3 1148A * 1225A Departed: 36 hours, 37 minutes late.
* RSV 3 1255P 3 1257P 141A 143A Arrived: 36 hours, 46 minutes late | Departed: 36 hours, 46 minutes late.
* SAC 3 213P 3 225P 207A 221A Arrived: 35 hours, 54 minutes late | Departed: 35 hours, 56 minutes late.
* DAV 3 244P 3 246P 237A 239A Arrived: 35 hours, 53 minutes late | Departed: 35 hours, 53 minutes late.
* MTZ 3 326P 3 332P 321A 323A Arrived: 35 hours, 55 minutes late | Departed: 35 hours, 51 minutes late.
* RIC * * 3 359P * 406A Departed: 36 hours, 7 minutes late.
* EMY 3 410P * * 415A * Arrived: 36 hours, 5 minutes late.