Dinny, if you haven't done so already, check with Revenue how a company has to pay the gross premium.
It used to that a company would pay the net premium to the insurer and then pay the balance to Revenue with their annual tax returns.
If that's still the case, then you can do as you suggest and have the company pay your policy directly, with them then charging BIK on the gross premium. Your membership certificate shows the total gross premium as well as the final net cost so the company should have all the figures they need from that.
There may be a small complication if anyone on the policy is over 60, because of the way that age bracket gets additional tax relief, but that may not apply in your case.
One other thing to consider if you go ahead as you propose is that there will be no direct communication between your insurer and your employer. So if a payment is missed for some reason, the reminder will go to you and so on. You won't be swamped with stuff, but just bear it in mind, especially if the price increases at renewal or the like.