You said this is an ESB, correct?  Assuming your client also met the gross receipt test, §31(c)(4) would eliminate the limit for TMT and, thereby, allow the credit to offset AMT (after reduction for credits other than other than the specified credits under subsection (a)).  It would appear that you may not have taken that into account.  The bigger question is whether the "Gen'l Bus credit" you mentioned is also a specified credit that is eligible for that treatment.

If you have entered the correct c/f details for the respective entities, Lacerte will correctly take into account not only the credit from CY but also c/f (as well as c/b) in determining the allowable credit shown in Part III, subject to §41(g) limitation.  The computation for each pass-through entity's §41(g) limitation for the year can be found on the respective Federal Worksheets (which should jive with your offline calculation).  The amount(s) would then flow to Part II, with the credit allowed computed in accordance with §38(c)(1) and (4) before it flows to F.1040.

It's working as I expected in my dummy.