They teach relatively little about this at Hurn.
As for the service the aircraft will receive after handover, that is a matter of negotiation between the pilot and receiving controller, so the handover becomes a little pointless, either way !
At my (Area) unit, we often transfer traffic to Mil units, but rarely with a handover, just having pre-noted details to them.
We do our best to call any traffic as they leave but as most traffic is receiving RIS that is all we can do.
I disagree competely about your "slackness" remark, YOU may be dealing with 3 or 4 aircraft in the FIR whereas we have 5 or 6 on airways plus several in the FIR on RIS.
It's all a matter of priorites, and I am afraid the FIR comes last.