As you need leave the sterile area to collect and recheck your luggage, you do require a visa, as you would have to go through Immigration.
When you say staff, if you mean airline personnel, no, but there are fee-based meet-and-greet services which can be booked in advance. In that case, you would be able to remain airside and Transit Without Visa, according to Timatic:
TWOV (Transit Without Visa): Holders of onward tickets for a max. transit time of 24 hours. In case of transit connections beyond 8 hours, passengers must remain airside and be accommodated in the airport transit hotel.
The Kuwait Ministry of the Interior notes that
A transit visa, valid for a maximum stay of 7 days, can be obtained from a Kuwait Consulate abroad or from a Port Authority in Kuwait. The fee is KD 2.
In Athens, the Kuwaiti Embassy is at Marathonodromou Street 27, Palaio Psychico.