95+% of navel/joint ill cases are caused by E.coli - and they usually indicate at least a partial failure of transfer of maternal antibodies: no colostrum/not enough colostrum/poor colostrum quality, got colostrum too late, difficult delivery resulting in poor absorption, etc.
I'd go with one of the broad-spectrum antimicrobials - ceftiofur, the active ingredient in Naxcel and Excede is effective against almost every E.coli isolate I've seen over the past 20+ years.
LA-200 would be a 3rd or 4th place choice, but way better than penicillin.
Supplemental Vit.A and Vit.E/Se injections would also be in order to help the calf's immune system function at a higher level.
Folks, if anything you treated with 'long-acting penicillin' recovered, it would have done so even if you'd just p!ssed in it's ear. Most people(including way too many veterinarians) misuse penicillin from the outset - I would not expect it to have any significant effect on E.coli in navel/joint ill or Pasteurella/Mannheimia in pneumonia cases, etc.
Theoretically, a 'long-acting' penicillin preparation sounds good, and indeed, the benzathine penicillin G fraction in the available long-acting pen preparations does maintain a blood level for at least 48 hours - but it never gets high enough to kill ANYTHING! But, it will give you violative tissue residues for an extended time period.
If you get ANY response from treatment with L-A Pen, it's because of the procaine Pen G fraction, which produces a therapeutic blood level(if you give an appropriate dose) for up to 12 hours, and then drops off rapidly.
It's a joke that 'long-acting penicillin' products are still on the market. If they had to pass muster with the FDA today, there's no way they'd be approved, because the pharmacokinetic evidence is that the 'long-acting' (benzathine penicillin G) fraction does not/can not achieve an effective, therapeutic blood, tissue, or fluid concentration.