Determining why a transaction log file is so large
the transaction log for the second database is staying around 300GB. Each transaction log backup is around 80GB. 


That sounds reasonable.  Your log file should have enough room to accommodate the log records between any two backups without growing.  And it's better if you can afford to skip a log backup, or accommodate an unusually busy period without growing.  Growing the log file requires it to be zeroed, which takes time, and there may not be space available.

So if you normally need 80GB, having 300GB reserved sounds reasonable.

If you shrink the log file after every log backup for a few days, you can probably shrink it, but I wouldn't go below 200GB probably.  Internally the effectiveness of a log shrink operation depends on which VLFs inside the log file have active records.  See Shrinking the Transaction Log and How to Shrink the SQL Server Log for an explanation of why it can take several tries to shrink the log file down to something close to the average log backup size.