Don’t quite understand why you need to battle with your HR department, surely it is only the HMRC rules/guidelines which need to be satisfied.
I would have thought there are three basic options open after the initial 12 month hire period on say a £1000 cycle;
1, Do not transfer ownership to the employee and let them use the cycle rent free until the value is nil.
2, Transfer ownership to the employee for a nominal sum, say £1. The employee then owes the HMRC tax on £249 collected via a P11d (£50 or £100 depending on your tax band).
3, Transfer ownership to the employee for the recommended valuation of £250 and incur no further tax liability.
Obviously, option 3 is the least desirable choice!